Wolfram Physics Project: Working Session Open Q&A Tuesday, Oct. 13, 2020

okay hello everyone so we are going to do a q a about the current state of wolfram physics project um maybe i can start by saying a few things about what's been going on um things are chugging along just just great it's a complicated thing because physics is big and there are lots of things to do more and more people getting involved we have our collection of research affiliates and junior research affiliates about 30-something people um all sort of connected uh to directly to us and um to the project and people working on all kinds of different things i would say there's a range of activities going on from the pure uh exploration of the computational universe kind of nks type things through to much more connected to direct experiments about physics kinds of things and a lot of mathematical physics uh connections in between so what's been uh and i guess another thing that's going on is the use of the formalism that we've developed for the physics project for lots of other applications and that's something i personally have have ended up in a bit of a rabbit hole um studying things about metamathematics and so on having realized that our formalism can be applied to those kinds of things that might seem like kind of a waste of time for the physics project but it isn't uh the key point is that the idea of multi-way systems turns out to be really general thing and multi-way systems are a way of thinking about kind of systems that have many possible alternatives what they do at each step but they're a more global way to think about those things and they're a way to think about those things that have concepts like causal graphs associated with them and so on things which have not really been introduced in other places where there are like multiple choices of how things can go and what i've been interested in particularly is trying to develop more intuition about this kind of new type of construct that we have multi-way systems well it's not really that new i started talking specifically about multi-way systems in 1994 but it's a difficult concept and it's something where there's a lot to understand about how to think about it intuitively and i think it's really useful to think about multi-way systems in the context of mathematical theorem proving in the context of games and the context of number theoretic kinds of things because each of these different ways of thinking about multi-way systems helps us get sort of closer in on you know how to understand this concept and uh for example i've been interested recently and thinking about game well game trees game graphs you know tic-tac-toe all the possible things that can happen in that how that relates to the structure of multi-way systems as a way to get sort of intuition about things in quantum mechanics and so on that also work like multi-way systems so that's that's for me been an important thing uh another big direction has been as i said the mathematical physics direction and uh jonathan gorad and other people uh in our team particularly have been um uh working a lot in that direction and um uh sort of the the big news there is the connection of our formalism to things that are kind of at the frontiers of mathematical physics in various directions in particular connections to the categorical uh description of quantum mechanics and essentially uh one uh part one of a multi-part series of papers with jonathan as lead author um just came out last week it's it's already a hundred pages of uh of heavy category higher category theory type type stuff um basically proving the equivalence it's one step in proving the equivalence of our formalism to categorical quantum mechanics which in turn is known to be equivalent to standard sort of von neumann uh formalized quantum mechanics which is standard quantum mechanics so that's an important step in kind of uh making all these connections between what we've been doing and what people have been thinking about in mathematical physics and there are a bunch of other things along those lines that are being worked on um i have to say i i i personally have also been been thinking about like last week i think it was last week um put out a piece about um understanding faster than light going faster than light in our models and the realization that in our models because space doesn't have the kind of simple structure that uh one has assumed it had for a long time in our models the problem of going faster than light becomes sort of a an engineering problem similar to sort of breaking second orthodontics behavior rather than a um a sort of pure physics problem but again exploring that idea led me to more intuition and more foundational notions about for example in that particular case how space is reconstructed from causal graphs and so on so an awful lot of kind of exploring the formalism and seeing it in other contexts which i think is very helpful i mean i personally am about to launch into two efforts uh one very well three efforts actually several efforts um one very practical which is what are the phenomenological the potential experimental consequences of our models that are uh you know uh potentially immediately accessible now now many of those things the actual parameters may be such that you can't uh you know you can't see them easily but the issue is how do we um how do we at least even conceptualize what kind of thing could you measure it'll be a lot of work to actually do the astrophysics do the particle physics whatever to figure out oh you should see this particular value of this particular thing but the first thing is just to surface what kinds of things might you be able to see and uh we we've done a few of those things in these working sessions but um that's another thing that that uh hope to pursue um another thing that's also more on the intuitional side is one of the realizations of our project is there are different views of physics that is the physical laws that we humans with our sensory inputs and so on a tribute to the universe aren't the only possible ones you could attribute to the universe and again as a matter of both intuition and uh and sort of philosophical understanding um i've sort of launching into an effort to understand the broader picture of what are some radically different views of the universe that you could have while still describing the same underlying computational processes um and uh let's see we already have um a few questions here but i'm i'm happy to to address lots of things um calais says i sent something to jonathan about suskin his recent work on information density it seemed relevant uh jonathan are you here do you want to comment on that uh i embarrassingly i don't actually remember this particular email exchange if it happened suskin has done some stuff i i don't so i don't know about this particular comment but suskin has definitely done some stuff that we think is is of relevance to the project particularly around um sort of a complexity theoretic view of the er equals cpr conjecture so there's this this idea in in sort of modern quantum gravity which is the einstein rosen equals einstein pedolsky rosen conjecture which is um hypothesizing a relationship between the entire okay if you have um if you have a pair of this is a this is a loose explanation but it hopefully will give you the intuition if you have a pair of entangled black holes then uh that pair of entangled black holes behaves a bit like a wormhole solution to einstein to the einstein field equations because essentially you can you can transmit information through one event horizon into the other event horizon through a quantum teleportation process and that works a little bit like how you can you know go from one point in space time to a different point in space time by following an einstein rosen bridge a wormhole solution and so the er equals zpr conjecture which comes out of ideas like holography is this conjecture that um actually these two things are ultimately equivalent that there's some duality between entanglement and you know and wormhole solutions i.e the large-scale geometry of space-time and in particular suskin and doug stanford and some other people have been responsible for formula for formulating a complexity theoretic view of that where the entanglement entropy of the two black holes which is basically a measure of quantum computational complexity is related to certain features of the classical bulk geometry of the associated wormhole and um that's so that that's a that's a sort of um that's a place in conventional quantum gravity where where people are starting to use ideas from theoretical computer science and where we think we have something to say about that where effectively we have a way of reformulating that correspondence in terms of a complexity theoretic view of the multi-way causal graph and we still don't know in complete detail how it's going to work out or whether it's going to completely connect with things that people like like susken have been doing but that's definitely a kind of a correspondence that we think does exist um but i should look maybe maybe you should say something about how you know the basic idea is the multi-way causal graph is something which relates branchial space and physical space which is essentially the story of holography the story of er equals epr and for us that's something which is just comes out because the you know in the multi-way graph there are branches that branching process is what defines the different uh the different states of quantum mechanics and so on um and the connection between those states defines branchial space which is sort of the state of space of quantum states but there's also the idea of physical space which is associated with um for individual states what is the what are the common what's the commonality of the hypograph between those individual states but the point is that in the multi-wave causal graph all these things are packaged together and so this er equals epr thing can be thought of as different projections of the multi-way causal graph at least that's the current uh i mean this is intuitively going to work out it's going to be a lot of work for jonathan and others to actually untangle the mathematics of what's going on but that's that's the intuition of what's going on i think right right and we should also say that there's in terms of the connection to computational complexity theory so that's something which in the conventional way of formulating quantum you know conventional ways of formulating quantum gravity is uh a somewhat unexpected counter-intuitive connection that you know that the entanglement entropy which is ultimately related to the to the computational complexity of a of a sort of quantum fourier transform operation that you need in order to reconstruct information from the event horizon of a black hole the fact that that should be connected to features of the bulk geometry of spacetime is not at all obvious in the conventional way that physics is set up but in our way formulating things it's much much more intuitive because both uh physical distance in physical space and distance in bronchial space as steven mentioned are really complexity theoretic measures in the sense that when you say these two points in the hypergraph are a certain distance apart ultimately what you're saying is that if i want to propagate a signal from one to the other there's a certain minimum number of rewrite steps i would need to a a number of rewrite rule applications i would need to do in order for that information to be successfully propagated so geodesic distances in the hypergraph and in the causal graph are really statements about you know computational complexity of certain information propagation uh sort of processes the same thing is true in the in the multi-way system as well because when you when you say that there's a certain common ancestry distance between two states you're really saying uh you know up to some factor of two there's a minimum number of rewrites i would need to apply in order to transform from from one state to the other if i'm allowed to reverse some of those rewrites um and so that the fact that both of these things should be connected to features of computational complexity theory makes total sense in this setup and the fact that that people seem to be rediscovering the same thing independently in these other completely different setups is i think a really really positive sign right i mean you know at this point we're sort of checking off there are these you know what's known in mathematical physics what's known in physics in mathematical physics there are various frameworks and we are steadily checking off you know how do they relate to what we're doing you know causal set theory how is what we're doing generalizing causal set theory how is what we're doing uh related to categorical quantum mechanics etc you haven't done string theory yet string theory remains out there and somebody should should really do it before before we get to it eventually we'll get to it but but um i kind of was was assuming somebody else was going to do that one um because it's fairly clear what's how it's going to work but um and it's going to be quite interesting it's going to give us a lot of a lot of intuition see see one of the things that i think is really interesting about what's going on is by having this framework we have this kind of way of connecting together these things that have been intuitionally very different which includes how to think about distributed computing versus how to think about uh physics and reference frames that's an important connection i think that in distributed computing you know we will be thinking about you know programming in reference frames we're importing kind of the intuition from physics to distributed computing and vice versa and you know it's those kinds of connections that i think are what will allow us to really make good progress because in the end you know it's it's really important to have these ways to think about things there's one thing is the technical details of how you actually work something out the other is what is the context what's the way of thinking about it and that's that's an important part of what's developing um i think uh uh yeah that was some so a bunch of questions here that oh i was going to say one thing about um about black holes and other things i mean one thing that i have to say i first wondered about when i was a quite young kid is you know are particles actually just black holes and we're getting closer and closer to that conclusion that in some sense particles like electrons and so on which in our models are features of space we imagine them to be some kind of topologically stable feature of space but i think you know the relationship between what's a black hole what has an event horizon what counts as a topological feature of space i'm not sure maybe jonathan has some some words of wisdom about that connection but i i think that there's an increasing sort of it's increasingly looking as if the kind of lump of weird stuff in space versus black hole are at least a very similar story right right i i agree that does that would be that does seem like a plausible hypothesis i mean for me the interesting question is um it if it's the case that you know the description of a black hole singularity and the description of a topological obstruction that is an element that we interpret as an elementary particle it could well be that those descriptions are actually very similar but the interesting question i guess would be in the elementary particle case do they end up being naked singularities or do they obey you know is there is there an event horizon of particles and if so you know what does that really mean what what in what in what are the implications of that for things like particle interactions well i think yes but my my belief about that would be it's the same kind of no hair story as black holes that is the fact that all electrons appear to be the same might be the same reason that all schwarzschild black holes appear to be the same that is that that you know an electron it could be the case that every electron might have its own personal story but it's inside its event horizon i mean that's a that's a in its own personal way to attach to the main part of the of the hypograph but it's inside its event horizon and so with respect to every external property of the electron it has only a you know a a definite form i think that's the you know that's kind of the intuitive idea but but really one of the things that that i would say we've been remiss in doing we haven't done yet is really going to hunt for particles we've kind of been waiting there are a few things that we're trying to do in in preparation for the hunt for particles which is the hunt for topologically stable structures in hypergraphs and so on one is max piskanov's work on local multi-way systems which has been going rather well um and where the idea is that you're able so one of the things that i keen on is this concept of multi-space this combination of physical space with branchial space where your you know what we've been doing so far is mostly talking about global multi-way systems that is um this is the this is the multi-way system where every node in the multi-wave graph is a whole state of the universe the idea of a local multi-wave system is that you get to kind of weave together only those parts the things that are sort of common to different states of the universe are all together and it's only kind of bubbling out in the direction of of things that are not common and that's this concept of multi-space and we've been trying to sort of start understanding multi-space um and it's just a very challenging thing to wrap one's head around or to visualize and so on but that's that's one thing is is the development of local multi-way systems um another another thing is that we've been interested in uh the origins of quantized spin for particles and also the origin of fermions versus bosons and we made some progress i think we have a good qualitative idea about how that works and it's just a bunch of heavy lifting mathematical physics to to really nail that down and i think both jonathan and i have been distracted by different kinds of particular projects um uh arguably mine are um well i don't know whether mine are less relevant or more relevant but but they're different at least um and so we haven't really worked as hard on on on that issue as we might i mean to give you a qualitative idea uh spin is quantized we know that you know the electron has half h bar of spin you know photon has one h bar of spin um etc um why is it quantized why is angular momentum quantized in our models we have a picture of what hangar momentum is it is my strong guess that there is a story of homotopy in the multi-way causal graph that will end up being some homotopy group type thing in the multi-way causal graph will end up being the story of why those quantize spin we'll see one of the important things about spin is this half integer spin and there's integer spin half integer spin is associated with fermions things with fermi statistics um uh integer spin associated with things with both statistics understanding that spin statistics connection and understanding even the idea of spinners half integer spins which are things where even if you rotate through 360 degrees you don't come back to the the the same thing again you come back to minus the same thing understanding that in our models so our current suspicion is that spinners are it's as simple as this spinners are associated with directed hyper graphs and uh the ordinary uh rotation group not the spin group the ordinary rotation group vector type things are associated with undirected things which are effectively undirected hypographs and they're kind of ways that one can model that involving taking limits of these kind of equivalence classes of regions in the hypergraph and looking at the limits of those equivalence classes and how they limit to things like lead groups and that's kind of a coming attraction that we haven't really done um and and the the whole question of both statistics versus fermi statistics um you know whether particles like to get together whether they like to stay apart our current guess is that that's associated with uh divergent parts in the multi-way graph and parts that converge in the multi-way graph the convergent parts being the bose-einstein statistics the the non-convergent pars being the fermi direct statistics that's at least the current uh the current thought about this jonathan do you want to add something to that no no i i think that's that's a pretty good explanation so i mean and and as the one thing i think that's worth emphasizing there which i think you kind of mentioned at the beginning is that this is a way of thinking about you know fermi direct versus suppose einstein statistics as a bulk feature of the universe right which is not conventionally how it's done i didn't mention that that is very important yeah i mean this this idea that this is the surprise one of the one of the many surprises of this project okay the fundamental meta surprise of this project is it's been a lot easier than i expected now that's a that's kind of one of these you know you shouldn't say that because you don't know what's coming next but um uh the um uh you know the thing that's been easier about it is i thought we would have much a much bigger hill to climb with computational irreducibility we will be able to say less the other thing i thought was that many phenomena that we would look at could not be found in idealizations so what do i mean by that i mean that to understand energy we would have to understand what electrons are and then we'd have to count electrons and look at the properties of electrons and so on to understand energy but one of the surprises of of uh before you know last end of last year i think um was the realization that energy and momentum can be thought of as bulk properties of the spatial hypograph the causal graph etc um and so is fermi diracness is the fact that things obey an uncertain uh an exclusion principle is that a bulk a statement that can be made in bulk or does that have to be made in particular in a pun i'm making a bit of a pun there because when i say in particular i mean only with respect to particles so to speak because we don't yet know how particles work and the interesting thing is it looks like we can make statements about statistics in bulk now that's not super surprising because after all we do have bulk bose-einstein systems and we have uh bulk formula ax systems too so it isn't in in quantum statistical mechanics both of those things are absolutely things so to speak um and uh so uh and i you know one of the connections here which we haven't really explored somebody looked at a little bit at the summer school is uh back in the day i had these simple cellular automaton models for the molecular dynamics of of gases and so on of fluids where you just have a bunch of discrete cellular automata uh bits going around a bit like molecules and then large scale limit the thing behaves like a fluid with continuous velocity field and so on well you can do the same kind of thing in a multi-way uh graph where where the where the collisions in your cellular automaton aren't deterministic but they have they have multiple possible outcomes they they they're not just they're not a single way system where where there's just a single history there's one where there's a branching history so that gives us i think a way to get from our models to quantum statistical mechanics and quantum statistical mechanics has uh notions of kind of bulk firming iraq bulk bose-einstein statistics and so i think that's a possible way into an understanding of firm direct statistics in bulk and so on i mean i would say in terms of these surprises the fact that we can understand quantum phenomena quantum mechanical phenomena not using our full hypograph formalism but just using string rewrite systems is very interesting it's not super surprising after the fact but it makes it a hell of a lot a lot easier to do these analyses that we can actually analyze the double experiment the um uh you know quantum teleportation these kinds of things in the context of these string rewrite systems without having to build this whole structure of space-time and by the way i should say that jonathan wrote up a little bulletin about the the um the double slit experiment and uh which has been uh variously um applauded and and and criticized for its apparent sleight of hand of you know how do you actually get to this answer and um it turns out that we're increasingly understanding how one gets to that answer and it's needless to say it's a pretty subtle piece of mathematical physics and uh and the fact that it was possible to barrel through and get to that result as comparatively simply as in that bulletin is uh it's interesting that and it's one of these things where it turned out to be easier than we thought the real story has to do with how do you make coordinates in branch hill space in physical space we have the notion of coordinates there's you know three dimensions of space and so on and bronze shield space formed from all these branches in the multi-way graph how do you make coordinates out of those that's hard to do and one of the surprises which seems to be being validated in multiple places is that one common thing that happens which is absolutely freaking bizarre to me at least is that there is a natural let's say two-dimensional structure to a piece of the multi-way graph but the actual coordination ends up being the result of a space-filling curve a one-dimensional space-filling curve snaking its way through that naturally two-dimensional structure which is really bizarre not seen before not the kind of thing one's seen in in other kinds of uh physics but that seems to be the way that sort of coordination in branchial space one of the one of the tricks of coordination in bronchial space now i think that the more official version of this is coming from jonathan and xerxes and nano's um work on on categorical quantum mechanics and um that's a much heavier lifting process in mathematical physics to understand how that all works jonathan any comments any any latest late breaking news about how that's working out uh not any particular news in relation to that but i i i should just say something about how that whole correspondence is working so in um so as steven mentioned right so the the there's this view that which we get from this project of you know quantum mechanics is kind of the the of what happens when you throw away the actual you know geometrical structure of the hypograph and you only consider the combinatorial structure of the multi-wave system and conversely kind of general relativity seems to be the idealization where you throw away the combinatorial structure of the multi-system and you only care about the geometrical structure of the hypograph so there are other uh there are other ways of formulating quantum mechanics that people have considered in terms of you know ultimately diagrammatic rewriting rules over combinatorial structures that produce multi-way system like objects and one of the most sort of famous ones is this thing called the zx calculus that comes out of categorical quantum mechanics developed by uh coco and duncan and um so the way that it works is you represent an arbitrary sort of linear map between qubits as this as this thing called a zx diagram which is ultimately just a it's a directed graph with with particular sort of tagging of the nodes um and then there's a rewriting language you can define over those graphs that's provably complete consistent and sound in the sense that uh you know two linear two linear maps and quantum mechanics are equivalent if and only if the two diagrams are rewritable are mutually rewriteable to to one another um and so what we've been working on is basically trying to sort of represent that in this multi-way system framework and show that that the multi-way system formalism is a kind of an abstract generalization of this idea um but one of the really nice features that we weren't really anticipating when we first started doing this but it's kind of obvious in hindsight is that these these zx diagrams basically have their branchial space already coordinatized because every zx diagram the the individual nodes which are called spiders in the zx diagrams have phase information associated with them and that phase information is one of the things that's manipulated by these rewrite rules um so so given a particular diagram and because branchial space is naturally laid out in terms of quantum phase given a particular zx diagram we already know a priori what its coordinate is in branchial space so in effect it's so unlike in the hypergraph case where we're trying to kind of figure out what the answer is in relation to this coordination problem the zx case is really nice because we know what the answer is and we need to figure out why the answer ends up being what it is and so it's in this particular instance that we've been able to show that the natural phase coordination of the branchial space of zx diagrams happens to have this space-filling curve structure that ultimately turns out to be related to the fact that the individual in in their operator form when you try and construct a composite phase for the overall zx diagram what you're essentially doing is you're applying a pairing function over the arguments in the individual the over the arguments of the individual operators for each spider and the and the the pairing function you're applying is some generalization of the cantal pairing function that is known to produce space-filling curves and and so this is going to submerge deep into this ocean of a great complexity here right this is hard to explain i mean yeah i could i could try and do my version of what i think is going on there but but um yeah it suffice it to say it yeah if you can look at jonathan's paper if you're interested in knowing what the actual story is right but that's the basic picture of kind of what we figured out so far and so so we think that so one of the reasons one of the many reasons why i think this this whole categorical quantum mechanics side project is worth pursuing is because i think that ultimately it's going to allow us to prove i think quite a general coordination theorem about branchial space it's going to allow us to kind of define a general procedure for you know given a particular multi-way system what is the procedure for assigning phase coordinates for each of the states you know the zx case gives you a you know a particular instance of a multi-way system for do of a multi-race system formalism which you can do that um but we that we have reason to believe that actually those procedures can be generalized essentially to any multi-way system and so that's a that's a nice kind of spin out of that of that project we hope will be coming quite soon by the way i just want to mention methodologically i keep on saying this project is going more easily than i expected but part of the reason for that is that you know we've got a stack of tools that we've been building for a really long time um that particularly i've been building for a really long time that are what make this possible if we look at some of the things that are actually going on so you know we're making increasing use of automated theorem proving for instance which is a fairly heavy lifting you know symbolic methodology which really has not been used that much for fresh research i mean i used it 20 years ago in finding the saxon system for boolean algebra but generally fear improving automated theorem proving is used sort of after the fact to to fill things in we're using it as much more of a primary you know actually figure out what's going on type of approach the other thing is being able to do serious computational experiments to both figure out what's true and develop intuition um is is really quite important and for us you know these seem like oh that's easy um those have been you know those are pretty much uh you know blocking items in terms of uh that have you know you know the good news is they seem easy to us and that's why we're able to make progress here but it's interesting methodologically that we're kind of taking for granted these things which are actually not common tools that end up getting used and it's interesting to me that these tools end up being as valuable as they as they seem to be to us all right we have many many questions here so let me start addressing some of these um okay question here from beauty first question could the cosmological constant be a rule instead of a number um okay so what is the cosmological constant so that has to do with what space is in our model space is the result of the these elements in this hyper graph being so sort of knitted together by relations in the hyper graph which are themselves defined by activity in the hyper graph so a way to think about it is the reason why there's a thing like space that seems to be sort of coherent and where you seem to be able to sort of move and in it is because all these sort of atoms of space have been knitted together by these update rules that connect different parts of space so if it wasn't if space if everything just stopped if the if the clock stopped so to speak there isn't a global clock but if the if the process of computation that is the rewriting of pieces of this hypograph if that stopped space would effectively fall apart there wouldn't be any sense in which you could say oh i'm moving from this part of space to another because that process of motion involves basically the the fact that the space that you you're you're doing operations in space in order to achieve that motion so in a sense space is a thing knitted together by the continual activity in the universe and the structure of spaces defined by that activity and the question of a cosmological constant has to do with what is the effective energy density of that space and that in turn has to do with in our model we actually think we know what energy density is and it has to do with essentially directly activity in this in the in the uh the amount of activity in this hyper golf and it's hard to define all this stuff because it's like it's activity in space but then you're talking about the density and amount of energy per unit volume of space but you don't have a notion of volume because that's defined by the structure of space etcetera etcetera etcetera so it's all a bit trickier and a bit slipperier but the end result is uh you know what's happening in the universe is most of what happens in the universe is the maintenance of space most of what happens in the universe is the knitting together of these atoms of space by these continual uh rewrite rules and in fact perhaps in our estimates of magnitudes of things all but one part and 10 to the 120th of what's going on in the universe is the knitting together of space and everything that we know and care about in the universe is just that little froth that 10 to the minus 120th piece on top of the major activity of the universe which is the knitting together of space okay so having said that the cosmological constant has to do with what is the zero of energy for space and is the zero of energy you know there's all this activity going on in space which is what knits together space but activity is also what produces energy so energy the the what you attribute to being energy in a particular part of the universe is the difference between the amount of activity going on in that part of the universe and the typical amount of activity going on in the universe so in a sense the cosmological constant is a story of what do you count as a zero of energy and the question of whether you can have for example changes in the cosmological constant things like this over the course of time whether different parts of the universe can have different effective cosmological constants those are all questions about is the is the structure of the spatial hypergraph how uniform is it you know one of my kind of weird things is the notion of vacuum cleaners which are regions of the of the spatial hypograph which have less activity than the typical those regions will behave as if they have negative energy density or from the point of view of gravity they will behave as if they're like dark energy they're like something that leads to a repulsive force of gravity a negative mass force of gravity but so that that's some but one thing we'd love to be able to calculate is what the cosmological constant is that would be a really cool thing to to be able to calculate um another thing we wonder about is uh you know how does the cosmological constant play out in branchial space instead of physical space not clear how does the expansion of the universe play out in barnstall space not clear um these are these are all questions that we're still we're still having to investigate i would say one thing about the cosmological constant that i actually think is fairly near at hand is this phenomenon called the casimir effect casmir effect is a phenomenon of quantum field theory so in ordinary quantum field theory one feature is that every quantum field whether it's an electron field a photon field whatever other field it is you think about that field as being a sum of pieces that correspond to sine waves of different frequencies they're the modes of the field a free field has modes that are just like sine x sine two x sine three x sine four x times five x etc and in the vacuum in standard quantum field theory there is at least there's half a unit of excitation of every one of those no modes so it's as if in the vacuum it's sine x plus sine 2x plus sine 3x plus sine 4x that represents in a sense the the um the activity of a quantum field there isn't the vacuum even in ordinary quantum field there is not a place where nothing happens it's a place where every mode there's a bit of every mode of the quantum field that exists but you say but that doesn't matter because it exists everywhere so when we say what exists somewhere we're saying what exists here that isn't something that exists everywhere what's the difference between what exists in in the formal language of of um of quantum field theory it's called normal ordering is the way of of uh that's a that's a trick for basically zeroing out those um all of those uh uh kind of activities from zero point uh fluctuations in these quantum fields okay so having said that if you were to make a box that had um uh metal plates for example just two plates big plates and you were to say okay i want to look at the modes of the field between these plates and the modes of the field outside the plates the point is that between the plates the any mode of the field that has a wavelength that's longer than the distance between the plates can't exist between these plates but it can exist outside the plates and so that leads to this strange phenomenon called the casmir effect which is a phenomenon where basically there's a force that comes because all these modes on the outside exist but they don't all exist on the inside and so there's sort of a pressure from these fluctuations in the quantum field um from the outside pushing in on these plates and it's an experimentally measured thing that that that happens i mean i should say that it's not actually as obscure as i'm making it sound because actually vanderville's forces that um uh hold are very relevant to holding lots of molecules together and so on are forces between molecules and so on those are related to exactly the same phenomenon there but they they happen to operate in the vacuum fluctuations operating on the um uh inducing electric dipole moments in in the distribution of electrons and so on and it's in fact the same kind of phenomenon um but in any case this casimir effect uh in our models we should be able to compute the cashmere effect we should be able to compute gravitational generalizations of the casimir effect the casimir effect in the interior of a black hole is something we should be able to start computing and i think that may give us some insight about the cosmological constant and um uh the way in which we can uh sort of uh uh sort of bulk properties of of the vacuum um that we can we can make measurements on uh let's see tucker is asking what's the current understanding of the standard model of particle physics using our model well gosh okay the standard model of particle physics has three basic elements a certain set of particles quarks and leptons and things like that a certain set of gauge fields and the higgs sector okay those are three sort of pieces of the standard model let's talk about each of them uh actually the one perhaps to talk about first is the gauge component the gauge bosons the photon the w and z bosons the gluons these are associated with these are the carriers of forces they are associated with uh local gauging variants okay we have been a bit remiss i would say in the last few weeks in investigating local gauge events we had a really good lead on local gauge and variants we think we understand basically how local gauge and variance works in our models but we have not explored it and we need to explore it somebody maybe jonathan can comment on on the state of local gauging variants and i know um graham was was studying this but i haven't i haven't heard what he's been up to for the last few weeks so we don't have a current um uh i don't have a current status on this but the i mean the the sort of the the bigger story is can we reproduce these sort of local invariances um in our models and can we understand the gauge groups that occur in the style model do you want to comment on jonathan you look like you again yeah sure so i can give something some quick explanation of how sort of um fiber bundles local gauge and variants kind of works in a discrete setup or at least a conjectural formalism how it can work so um one thing you can do is you can start from a from a total space that is discrete so you just start from some set of discrete points you call it a total space and then you you define a discrete gauge group over it like you know the icosahedral group i think is stephen's personal favorite example and then you and so you look at the the group action on on that space and in particular you look at the orbits of each point right so that the because of so we're going to explain this to people we have to go much lower let me let me try a version of this okay so first thing is if you're thinking about an electromagnetic field like an electric field in space how do you think about that the answer is at every point in space there is a value of the electric field that is defined by a vector which has some direction that direction is a direction that is not a direction in it is a vector that points in a direction in space but it is not a vector that you can think of as being in space it is a it's a it's a it's something where at every point in space there is a there's a vector sort of attached to that point or in general with electromagnetism l i'm kind of cheating for electromagnetism actually because in electromagnetism the real story is there's this there's this phase uh associated with the u1 gauge group there's this there's it's like where are you on a circle but that circle is not something laid out in physical space that circle is in the space of the gauge group but there's a version of that circle there's a copy of that circle associated with every point in physical space and the mathematical structure that one says one has is a fiber bundle where this gauge group the degrees of freedom associated with the electromagnetic electromagnetic potential are are the things that exist in the fiber and there are fibers it's like a carpet or something where there's a fiber at every point in the carpet so to speak the base space is physical space and there's a fiber that represents this internal uh what what can exist internally and it's the the internal degrees of freedom the internal sort of motion within the fiber that's associated with the gauge group okay now now that i tried perhaps unsuccessfully to to explain what what a fiber bundle is um the the uh uh you can no now go back to you you were talking about this version go ahead yeah right okay so so the really nice thing is that the continuous setup that stephen has described which is the standard sort of way of thinking about gauge theory has quite a nice discrete extension so in this case you the the total space that you start from is now a discrete set of points and the uh and the gauge group is no longer a lead group it's some some discrete group like the like i said like the icosahedral group which is some approximation to a rotation group and um so what happens is that there's this theorem kayley's theorem that says anytime you have a discrete finite group it can be thought of as being basically a permutation its action can be thought of as being a permutation so when you define this disk when you just find this discrete gauge group over your total space what it's doing is it's just taking the points in that space and permuting them relabeling them and so what you can do is look at uh so and because the space is finite there's only a finite number of points uh there will be a finite orbit so you know point a will be relabeled to point b point b will be available to point c and so on and eventually you'll get back to point a and so what you can look at are the orbits of each point in the total space under the action of this gauge group and those orbits form loops in this in this other combinatorial structure and each loop we refer to as being the discrete analog of a fiber and therefore the overall combinatorial structure that contains all of the loops all of these orbits is the fiber bundle and so one of the really nice things about that is that it preserves all of the standard kind of algebraic and geometrical features of gauge groups and fiber bundles in the continuous case so for instance it's known that if you take the if you take a fiber bundle you mod out by the by the group action then you get back to the base space and that's exactly what happens here and um in the same way there's this notion of a connection that exists in gauge theory which is a rule that says if i if i make an infinitesimal step in the base space that should be lifted to some infinitesimal step in the fiber bundle and the connection is the rule allows you to do that lifting and here again there's a very very direct discrete analog of it which says if i have an individual edge in my in my base space i can lift that to to a net to an elementary edge in the associated fiber bundle and and we have rules for doing that so so graham during the course of the summer school constructed a kind of minimal example of this for for a particular um hop vibration a particular sort of topologically non-trivial version of of of one of these fiber bundles for a for a non-trivial gauge group and it seems to it seems to be correct uh you know there seems to be a legitimate way of doing of doing things and the the reason why this gets really interesting is because local gauge invariants the statement that the that your spaces are in very that so for each for each fiber there's a kind of collection of of possible coordinate bases that you can pick and local gauge invariant is the statement that kind of ultimately the structures of your spaces don't depend on which coordinate basis you choose for each fiber so in our case each each coordinate basis because of the way the connection works each coordinate basis is associated with a particular hyper edge which is our in the hypergraph that's our base space and in and each hyperedge is in turn associated with a particular orientation of your rewrite rules and so local gauge invariance reduces to the statement that the structure of your of a space like a causal network is independent of the orientations in which you apply your your replacement operations and therefore is directly related to causal and variants it's kind of a it's a weaker version of causal invariance um and so that's why this version of that argument jonathan that's cleaner than i've seen before okay good um yeah thank you well yeah so we're making gradual progress towards kind of conceptually understanding what's going on but but uh yeah what we need is a kind of complete mathematical theory uh that allows you to map concepts in continuous gauge theory to concepts in this discrete set up and we don't we have particular cases we don't yet have the we don't have the general you know we should do one of these working sessions looking at local gauge and variance because i think we should construct some more we should just have a a a kind of production line of examples of um i mean you know we have this one example of the hop vibration but we should have a production line of examples of these because i think that will give us you know give us more intuition i mean it's a we're going against you know alan turing wrote a paper about um uh approximations to lead groups continuous groups uh finite approximations to continuous groups in which he basically concluded there isn't a way to do it you're out of luck there aren't finite approximations to lead groups i think we are for once we're about to prove that alan turing was wrong about something um and uh uh um you know because we have what amounts to a way of approximating league groups using although he was considering the case of just a league group is sitting there we're considering this case where there's fiber bundles and connections and so on which is arguably a more complicated case but but uh probably has a limit that gives you the the original e-group thing um i mean but by the way i mean the general idea you know lee groups are sort of the the they are continuous groups like the rotation group in three dimensions as a lead group which has where you can rotate just an infinitesimal amount as opposed to the group of the icosahedron look at this i'm actually going to be able to demonstrate this look at that there's an actual high cost agent what do you know and the whole point is that that with the icosahedral group there are only particular discrete transformations that will keep that will map the cyclosahedron to another precise cyclosahedron that don't just ended up in a different configuration but they're they're ones that end up with just oh that's just another i you know it's just the icosahedron again and that that difference between the uh the question of the the continuous group where you can have infinitesimal changes versus just the discrete group where you have discrete jumps like you might have for a square or something like this um how that limiting process works it's interesting what is i think an interesting analog is that what we've looked at in the spatial hyper graph where we just look at when you have this graph and you look at a large enough version of the graph with enough nodes you can think of that like a continuous space so similarly here this is like a large enough bag of discrete permutations can be thought of as a lead group and that's the thing i i will explore that a little bit in the in the stuff we wrote um i wrote just just before we launched the project but but we we need to explore that some more um oh okay the the third part of this will be the higgs sector the way that you give mass to particles um i don't think we have anything profound to say about that yet um other than that the notion of things like spontaneous symmetry breaking is closely related i suspect two features of uh you know the way that space is knitted together in our models but but the details of how that works we do not yet know um okay it's a question here digging deeper into alien intelligence is in the sense of different world views different perception systems could be parallel to the fact that artificial neural nets have a large number of minima um skeptical but possible let me explain what i mean the you know how do we think about the universe well one thing we think about is we think about space and time we think about the notion that there is a definite that things happen at a particular moment in time that is that we look around and we say the tree is moving this is doing that at this moment in time but in fact things at different places in space the fact that we view things at different places in space as all happening at a single moment in time is a feature of our way of perceiving the universe it's a feature of the fact the speed of light is fast compared to our brain processing speed at least for the distance scales that we're dealing with it's it's related to other features of the way that we perceive the universe we might not perceive the universe that way it might be the case that every separate event that happens in the universe that happens at a different space-time point in the universe was something separate that we don't bucket it together as these big slices of space at a particular time and so on that's an example of a difference i mean another another big difference is this notion of what uh we say oh we can just think of lit you know water as a continuous fluid where all the parts of the of the water of the little you know thing of water or something every every every sort of point in this water is sort of the same except maybe it has a different velocity of the of the water or something like that but in actuality there's individual molecules bouncing around there and the particular detailed configurations of those molecules are completely different in particular places in the in the water but in our view of physics we just say oh it's just a continuous fluid where it has the same property at different places we don't consider all those discrete molecular motions so a question that one might ask i think you're asking is an interesting question if we're using neural nets as a way of understanding what's going on in the world do they reproduce do they have the same prejudices that we have do they also bucket space in the way that we bucket space and so on do they also would they also take all those discrete molecular dynamics and say oh it's like a continuous fluid okay here's the situation i think the answer is probably they don't have to the fact is that what we have done when we have neural nets and we train them we are training them to connect what they do to our version of of how we perceive reality that is we train an image identifier to say that's a picture of a cat that's a picture of a dog not training it to say that particular pattern of fur on this thing is of this and i don't care whether it's on a cat or a dog all i care about is that particular weird pattern of fur or something and so i think that that the the what we have done to date with our artificial neural nets is very much we train them to connect to our view of how the universe works now could they connect to a different view of how the universe works is uh to some extent i think the answer is yes i think that they already have certain prejudices built into them because i think that they already have certain assumptions about continuity and calculus and so on built in which are particular to our way of viewing the universe and might not be general to any possible way of viewing the universe but i suspect that their views of the universe are more general than the ones that we humans have so far constructed but as i say when we actually use artificial neural nets we're always training the neural nets to be doing things which are useful for us which means they have to relate to concepts that we have like cats and dogs and so on that's an interesting question um let's see question from james here have you considered that events and branching could be converging rather than diverging actually in our models the whole point of this phenomenon of causal invariance is that every time there's a branch in the multi-way graph there will eventually be a merge in the multi-wave graph as well and that's critical because it means that you can there is some invariance about history that is it doesn't matter you know you couldn't just say oh we went on the wrong branch all is lost the world will never be the same again the answer is the world will always be the same again because of causal and variance because there is always a merge in the future okay questions here from that have come in from our site let's see a question from daniel has the number of abstract elements in the universe being constant since the big bang or are they created and destroyed uh strongly suspect that the number has not been constant we don't know that for sure but we strongly suspect that the universe is expanding in branchial space in in the spatial hypograph in all senses the universe is expanding as in it's getting more elements more atoms of space in the universe we haven't proved that but that's what we suspect is going on um the uh question here is is um uh is the expansion universe associated with more abstract elements coming into existence but basically yes we think that's what's going on um and uh it's a little bit of a you know i hesitate slightly because a little bit of a more complicated story because what matters is things about the causal graph and that has to do with events that happen in the universe and the question of the trade-off between the number of events and the number of elements is a little complicated but i think the basic bottom line is yes space is expanding because there are more atoms of space basically um let's see the question here from john uh is it a crazy idea from the successful lagrangian approaches to physical theories what about methods that generate models that are not self-adjoint uh some models might explain things like dark energy being contained in variant spaces those generalized eigenvectors and nil potent operators so i i think um you know it's a bit of a tricky story because non-self-adjointness there's there's a there's a question of unitarity probability conservation there's a question of time reversal symmetry which is those are different questions time reversal symmetry isn't in fact true for the physical universe since probably not what we're talking about the main thing about sulfur jointness of operators has to do with what amounts to probability conservation that the sum of all probabilities has to be one and that's a i think that's a matter of definition i mean in our models we have this sort of counting of pathways in the multi-rate graph and that counting of pathways gives you just integers but when you say well what's the probability of something happening you're normalizing it across all the pathways in a particular uh slice of this multi-way graph that you're taking jonathan do you have a crisper version of this no i i think that's a pretty good explanation of what's going on in our models but i think it's also worth bearing in mind that um we don't even know whether hermeticity is true even in the conventional way of formulating quantum mechanics so there's this whole field of what's called pt symmetric parity time symmetric qm or non-hermitian qm that was largely sort of pioneered by by people like carl bender which comes from the realization that you know to guarantee parity and time symmetry you your um your hamiltonians don't actually need to be hermitian they just need to have all they need to have entirely real spectra and hermeticity is is a sufficient condition for that but it's not a necessary one and so uh you can actually have these non-hermitian parity-time symmetric hamiltonians which violate algebraic unitarity and so in it on the surface might appear to be incompatible with quantum mechanics but actually from a physical standpoint they are still sort of pseudo-unitary in the sense that they still allow given a an evolved quantum state you know kepsai t for some uh positive t you can always reconstruct kept psi zero which is kind of ultimately the thing that matters that's why probability conservation and things are so important they're just they're measure preserving statements about your hilbert space that mean you can always reconstruct the initial state and so even in order in the even in the ordinary mathematical setup of quantum mechanics it's possible to make a perfectly sensible theory where your hamiltonians are not self-adjoint and your operators are not strictly unitary and still everything kind of works and probably what's happening here is is similar that our model there's no reason to believe that the the operators that we're dealing with in in the context of these multi-way systems satisfy exact algebraic uh hermeticity and unitarity but what they do satisfy as stephen said more or less axiomatically are these key measure-preserving properties which are basically properties about conservation of pathways in a multi-way evolution graph um and and for in terms of reproducing the predictions of quantum mechanics that's really all that matters let me ask a question i i don't know i mean in the interaction between general relativity and quantum mechanics in the past there were questions as i recall about hermaticity in that case too but i suspect that's just a big mess of what it means to have you know what the what the simultaneity surfaces are and what time is and probability conservation associated with different foliations of space time and so on so probably that's not that's not that interesting for us but am i am i correct in remembering that there was a big model with with quantum mechanics in general utility as well yes there there is that that confusion and actually in a in a way it's a confusion that we implicitly face too um it's the the fact that this story about foliations and reference frames does not play well with the standard mathematical setup of quantum mechanics is basically what you're referring to the fact that which you know which hilbert space of quantum states you see is dependent on your reference frame but all but you know all of those hilbert spaces should be measure preserving that places kind of unreasonably strong restrictions that don't actually seem to be correct and and so the the basic reason why that's happening is because the mathematical setup okay the basic problem from my perspective is that there isn't the ana that there isn't an analog of a lorenzian manifold for quantum mechanics so larency and manifolds are lovely in relativity because they allow because any individual slice through an anti-chain of that lorenzo you know through an anti-chain of the causal partial order for that lorencian manifold will give you a particular romanian manifold which is which is a you know a particular version of space and the lorenzo manifold itself is a version of space time but in quantum mechanics you kind of just have your hilbert space and that's a that's an instantaneous thing and this notion of a time extended version of a hilbert space that you can sort of foliate in these different ways that's not something that people have really explored and yes so so as stephen as you mentioned people had tried to develop you know geometrical structures based on anti-symmetric metrics and these weird non-hermitian operators that tried to get some distance towards formulating that in in the ordinary setup but didn't quite succeed you know that's an interesting point you make but the hilbert space is the basically spatial slice of the time evolution which we have in the multi-way graph um and so what we should be able to have is a generalization of hilbert space just as lorenzo manifold's generalized euclidean manifolds we should be able to have a generalization of hilbert space that is essentially a time generalization of hilbert space exactly right so so in the way that we think this kind of works and well we have proof that it works at least in certain cases um the individual branchial graphs that you see which are the instantaneous time slices act like the instantaneous hilbert spaces from ordinary quantum mechanics so the overall multi-wave evolution graph is this time-extended version it's light as as you mentioned it's like the laurentian manifold analog of a hilbert's space okay so what's the analog analogy between that and twister spaces so that that's where it gets kind of interesting i mean we we we don't know but the the one of the features of the correspondence spaces that you you get in twister theory is that they there there are from a particular twister correspondence face there's a vibration that gives you basically a projective hilbert space and there's a different vibration that gives you essentially a you know a complexified mankovsky space um and so we think although it hasn't yet been made very concrete that has something to do with the fact that if you take our one of our multi-way causal graphs there's a projection that will give you space-time a particular space-time causal graph and there's a projection that will give you the multi-way evolution graph which is as i say like this time extended uh version of projective hilbert space okay so are there discrete approximations to the twister spaces that's a good question i i genuinely don't know i haven't seen one but but it would surprise me if there have been that seems like something we would have found but i i'm not aware well so the question really for us is can we construct something can we you know can we look at our multi-way graph a multi-way causal graph and look at a limiting case of that and just as there are tests that we can apply for whether our thing behaves like you kill in space and d dimensions can we all or minkowski space in you know d plus one dimensions or whatever can we similarly apply some some aggregate tests to our multi-way causal graph and see whether it behaves like twister space so in other words what is the analog like dimension for example is a is a thing that we can do to sort of measure or we like euclid in space what's the analogous thing for a twister space go ahead we can do the same thing just with with the dimension being complexified well but complexification is a mess i mean we don't want complexity we don't want complex coordinates particularly but we can probably turn those into some other kind of coordinates right no no but but the the key thing that i mean the the thing that's nice about complex coordinates is kind of from a geometrical point of view we know how they should work right because you know in standard you know cp4 to er or pt2 twister space um you would you have four complex coordinates and we know that geometrically those will behave like eight real coordinates but with a slightly funky multiplication property and that's something that we should be able to test just using we should just go look for it if we didn't have all these questions on our live stream right now we could go look at it right now but yeah it's something we should definitely look at because that's that we can generate i mean multi-way causal graphs are not your most simple-minded creatures but probably well the question is are we going to be able to get anything we're going to need to do them from hyper graphs we're not going to be able to do them from strings do you agree i think we're the only way we're going to get what's that i agree because you you need higher dimensional objects a one-dimensional space is not going to do it right so it's going to have to be a genuine multi-way cause of graph those things are pretty complicated creatures um i mean even our minimal examples of them are pretty complicated but but um that doesn't mean we can't look at them and then the question is what we need is the test for these you know the complex coordinates test the test for do we have and to end complex coordinates and that that should be we should be able to measure just like we can measure a ball okay so what happens to a gdc ball in that situation can you can you talk about a property of a gdc ball when there are two n complex coordinates yes you you you can so uh i i you presumably you mean n complex coordinates and complex coordinates 2n to n it will behave like it will behave a bit like a geodesic ball in a 2n real coordinate space but there will be a con there will be an additional basically something that acts like a contraction map that results from the from the multiplication from basically from complex multiplication um i i don't know off hand exactly how that formula works but i know that there is one there is there is a direct analog of that so so in other words when we look at the volume of that ball we'll be able to see various kinds of or actually probably have certain symmetries of that ball that are associated with the fact that these are supposed to be complex variables exactly there's a there's an additional symmetry that wouldn't exist in the 2n real dimensional space because of the fact that certain multiplications of complex numbers are equivalent that you're basically there's there's a uh there's basically there's a spherical symmetry that's imposed by complex multiplication uh that you have to take into account okay i bet we can find that i bet we can find that i bet that will end up being a property that is an inevitable property of the multi-way causal graph possibly because of causal invariance i'm not sure right that they'll be or or even it may be more more structural more kinematic than causal invariants that there's that there's an inevitable feature of the very construction of a causal graph that leads to that kind of thing right all right let's go we should go find that okay by the way i should just quickly mention uh that there's a thing i was working i've just been working on very recently as in like today that's related to this in the sense that uh it's okay so so this geodesic ball way of measuring volume is a very sort of it's a nice robust way of measuring volume um but that and therefore of inferring the dimension of a particular causal network um or in the causal network case it's not a ball but it's a you know the same basic idea but there are many there are many sort of alternative methods that people have kind of proposed for doing this in the discrete setup and they have inter they have different properties that are sort of characteristic of the methodology and one of these is this thing called the mirheim maya dimension estimate um which is a which which gives you in the real case we'll give you the same uh sort of dimension estimate as the geodesic ball volume thing uh but in the complex case it will actually give you a different answer and that's so that's that's an instance of something we of a test we can potentially apply uh in order to yeah so actually if i can just quickly share screen i can show you very quickly how that works and we can move on something else but basically what's happening is in the okay so here are some here are some causal networks that i've constructed so they are explicitly kind of faithfully embeddable into into minkowski's into makovsky space so this is a two plus one dimensional minkowski space that's been represented using a transitively reduced uh causal network and then so what we're basically doing is you you're asking the question if we pick two events at random what is the probability that they are related by the causal partial order in other words what is the probability that there exists a directed path from one to the other in the causal graph and uh of course so and that's that's essentially the question of if we sampled points randomly in a space time what's the probability that they would be non-space-like separated and that turns out to be a function of the dimension um and and we if we solve this somewhat um somewhat complicated equation using n minimize we can compute so this is telling us that this is f given just a hundred points this is estimating the dimension to be approximately three uh well to be 2.75 we know in reality it should be approximately three and you get so so you you you see uh i think in this case a quadratic convergence to the actual dimension and so this is a three because you sampled those points at random like in a causal set type thing and sample them in three-dimensional space exactly so yeah so this is a this is a two-plus one-dimensional minkowski space which i've uniformly sampled using a pass-on process um so we so and therefore you it's nice because you can prove that the resulting causal network is is faithfully embeddable into that space um and and then and so this is a radically different way of doing dimension estimation there are some others that i've implemented like the midpoint scaling test and other things each one has its own kind of set of features and pathologies and the interesting thing is that that all of them behave slightly differently when you go to these weirder spaces like complex you know ones that involve complex coordinates and so that's you know something we can try to we can start to use to distinguish between you know twister spaces versus just ordinary space times yeah it's really interesting i i think that the yeah pity you weren't using 12-2 though or maybe you work as it now has spatial statistics capabilities and you could actually do a press-on-point process directly i was using 12 but i didn't know that was a feature yeah it's a whole there's a whole s section of spatial statistics although it's definitely euclidean space spatial statistics well it's not you pl you could in space because you can do it on the surface of the earth as well but it's basically um uh it's manifold type type stuff um cool okay well let's see let's keep going here uh robert is asking what's been the biggest surprise since the project started the biggest surprise has been a heck of a lot easier than i expected i mean i really didn't think we'd get anything like as far as we've got as i say these these idealizations that keep on working even though i thought we were going to have to you know advance to another level of of sophistication turns out you know 20th century physics was you know managed to figure out these places where you can successfully sort of make statements even in the face of all this computational irreducibility and so on i would say um i'm kind of it's interesting sort of we're seeing you know the other big surprise i suppose since the beginning of the project is the connection to these other areas of mathematical physics the fact that that the things we're doing seem to sort of form a rosetta stone for all these different approaches to mathematical physics that i thought were just completely separate kinds of things and the other surprise is that this formalism is ending up being related to all these other areas that um i mean look basically the story is this cellular automata are the minimal approximation to parallel computation where you know the structure of space and time and they have many many uses many more than one could ever have imagined this is the absolutely minimal model where you don't have any space and time and where you have kind of arbitrary relationships between events where you just have events happening that have arbitrary connections between them and needless to say i mean like for example uh well max had just generated here i'll show it i can let's see if i can pull it up um let's see if i can get one of these okay you'll see it here hopefully let me just see if i can pull this into something um humph see if i can get this how do i get this to be um oh there we go yeah i can show this let me share something here okay this is uh courtesy of max very recent um so this is the beginning of being able to animate the behavior of um uh one of our rules showing uh progressive updates and trying to keep kind of the structure of the hypergraph um i mean more or less i mean all that wiggling around that doesn't happen in the real universe all that happens in the universe is just the connectivity of this but this is kind of um showing sort of what what happens in this model and can see things going on here okay so you know i looked at this yesterday and i'm like oh my gosh you know our model is actually going to be good for embryogenesis as well because this is exactly the type of thing you see happening and the minimal models for embryogenesis are a bit complicated and you know people have tried to use cellular automata at certain stages where you have a real sheet of tissue that exists then you can use cellular automata but when you don't have the structure where space your structure is still not defined you can't but this is a place where we absolutely have it's like these little little little updates are just like the mitosis of cells and so on and i suspect one's going to be able to make a model for embryogenesis this way which is again just like a completely bizarre thing that wasn't at all expected but that's a feature of of having developed what ends up being a pretty general model for things as a question here does the theory have testable outcomes which prediction is most likely to be discovered first it has it has all kinds of outcomes that are both theoretical predictions and experimental predictions the the job of figuring out you know what the experimental implications are is pretty hard it's always hard for any for any serious theory that's hard um which one will come first i'm kind of guessing some of the cosmological ones will come first and not the quantum quantum computing ones and so on but i might be wrong it really depends on there's one scale we need to know which is the maximum entanglement speed which is the analog of the speed of light in bronchial space and we don't know that value if we knew that value we will be able to make all kinds of very quantitative predictions but so for example a typical example is the expectation from these models that there have been dimension fluctuations in the history of the universe now when those occurred and how big they were and so we don't know but just looking for dimension fluctuations that might have existed after the formation of the cosmic microwave background that's an example of a type of thing to look for if we find them something really weird is going on that strongly suggests a model that our model has to be right but then you know can we get a quantitative version of that not clear um you know we can we can know things about polarization of photons coming from the cosmic microwave background that will have been different if they had different numbers of polarization states if they traverse the region of space which has different effective dimension those kinds of things there are also possibly some predictions and jonathan we haven't looked at these recently much the things about photon correlations for photons in orbit around black holes that's one that i think is is quite promising where i mean it's kind of ironic that einstein for general relativity had the prediction that the bending of light around the sun would be exactly twice what was predicted in the newtonian case um and he was very lucky that that was a scale invariant prediction it was just a factor of two other things that he might have tried to predict would have involved knowing the value of the cosmological constant these kinds of things which he didn't know and so those wouldn't have been things that were predictable but but he got he was he lucked out and that he had one prediction we had one qualitative predictions like the existence of black holes although that wasn't understood for nearly 50 years um but uh the um you know the qualitative predictions like they could exist singularities in spacetime we have qualitative predictions like that as well um like this dimension change thing and so on and a whole whole boatload of other ones um but in terms of quantitative ones you know he lucked out in the scale invariant one i think we might have a scale invariant one that is bizarrely similar which is has to do with photons in orbit around black holes and the question of what correlations exist between multiple photons in orbit around black holes and whether the correlation between which is a sort of a story of the relationship between physical space and branchial space i actually haven't thought about this for a couple of months and we really need to work on it um and we we don't know but but um so so my guess is that the first uh there will be suggestions oh you should look for this and those suggestions uh some of those may may pan out probably in the cosmological domain first um then there will be the this particular value of this thing will probably come later unless we luck out in some scalar variant predictions um eventually when we start looking at particles maybe we'll get predictions about some well we should get predictions about particle masses and all the rest of those kinds of things but that might be pretty heavy lifting it might require it might require computations i mean as i say so far we've lucked out the things have been easier than i expected um that one we'll see we'll see maybe we'll be able to get particle mass predictions without doing sort of full heavy lifting of of um of working through cause sort of computational irreducibility and in fact this idea of correspondence between particles and black holes suggests there might be some sort of universal statements to be made there just as there are universal statements to be made about properties of black holes and singularity theorems and so on um uh has the question of preservation of information uh maintained during the evaporation of black holes been addressed yes we think we do understand that um we think that the information paradox for black holes which is the statement that quantum mechanics sort of preserves information yet in a black hole things are sort of fall into the black hole and disappear in the singularity or disappear behind the event horizon um that you know how can that be consistent um in our models the this qualitative picture needs to be worked out more precisely but i think it's pretty clear how it's going to work out is that there is a a causal event horizon and there is also a branchial event horizon um and these are two different or entanglements around horizon these are two different horizons and that essentially what's happening is that the information that the black hole has when it forms is trapped between the uh entanglement horizon and the causal horizon and that it is preserved in that zone between the entanglement horizon and the causal horizon for the lifetime of the black hole and on on black hole evaporation just comes back out again and um that is um uh the entanglement horizon so that the causal horizon is a horizon beyond which uh you don't get to send signals back the entanglement horizon is the horizon beyond which basically you don't get to make your mind up about what happened quantum there's no classical way to make your mind up in other words at the entanglement horizon just as you were sort of stretched at um uh you know tidal forces stretch you in in physical space so in a sense you're being stretched at the entanglement horizon to the point where your classical mind sort of can't make its mind up about which quantum thing happened and so so the the sort of the picture is that the um uh that their effects at the causal horizon that are classical effects that sort of can't get out of the causal horizon but the effects the at the entanglement horizon there are quantum effects that can kind of go through the entanglement horizon but cannot be classically uh they sort of can't classically escape from the entanglement horizon um that's a at least a rough way to say it jonathan anybody do you have a crispr way to say that no no i i think that's i think that's basically right that yeah the the the the sort of the hawking process is just the leaking out of of microstates that correspond to particular you know global multi-way states from an entanglement horizon which exists because of the presence of a causal horizon yeah i think that that's that's our current sort of as you say the current qualitative picture for how that will work out um but actually i started you know a couple of months ago i started exploring specific black holes and doing actual experiments to find different structures of black holes the main thing i discovered is that black holes are not as simple as you think black holes in a model where with discrete space time and so on have all kinds of interesting effects that are and their structure is complicated and you get have black holes inside black holes and things like this which you can also get in general activity but it's less clear what's going on i mean what's very beautiful in our models is the space-like singularity at the center of a schwarzschild black hole is just the termination of rewriting rules so in other words time ends just like in a when you when you if you if you hit the singularity if you're if you get inside a schwarzschild black hole a non-rotating black hole you are inexorably led to the singularity in other words the future of everybody is to be at the singularity and you see that absolutely explicitly in our models because all the paths of the lead of the causal graph just lead to termination time stops it's as if you know where you're going along and it's like everything dies time is just time is time stops nothing happens um the uh so so that's a um uh so you can kind of see those things but but then you see some additional effects so one effect i haven't really explored properly is what i was calling black hole wind an analogy to the solar wind so it's a it's a continual momentum transfer outside of the black hole that you could think of as being graviton hawking radiation um it's a it's a radiation it's a quantum radiation a quantum gravitational radiation and i don't know whether people have studied that in traditional hawking radiation i mean one would expect graviton radiation but but since gravitons play so badly with standard quantum field theory i'm not sure that's been properly investigated but um well you know what this is is basically a a momentum transfer out of the black hole associated with essentially unpaired graviton uh vacuum fluctuations um and that's that's an example so i mean that would be an example probably of a prediction of our models which is really an inevitable consequence of discreteness of space space-time i think um but needs to be investigated a question from uh kik can this somehow be re related to amplitude of hedonic amplitude ahedron theory um good question probably yes i don't think we know exactly how and i don't think we we need to um uh talk to nima and friends about um uh more about amplitude ahead theory i think uh the um uh um it's been a couple of months since i exchanged email with those folk and i i think i don't know jonathan any words of wisdom about amplitude ahead okay yeah so um i i don't know because i'm not i don't know that much about quantum field theory i'm not totally familiar with the with the physics of how the adolescent hydrogen works but from a mathematical standpoint uh it does seem like it it's a it's a relevant kind of structure so so um the amplitude is a way of computing scattering amplitudes in quantum field theory particularly in um in certain types of topological string theories in twister space uh using this this structure which is a which is a positive grasmanian which which has this representation as an amplitude and the reason the amphitheatre is is interesting that this positive grasmanian is interesting is because it's generalizing okay so if you have if you have a projective space you can construct a simplicial decomposition of that projective space and so you know you're you're doing this this topological decomposition into into these individual simplices which are just these simple kind of combinatorial structures now the the projective grasmanian which is the sample twohedron is some kind of generalization of the concept of a of a simplex um to a to sort of arbitrary polytopes that exist in algebraic geometry and uh and in particular to this to this particular uh grasmanian space that's that's used in in the context of twister theory and so it's one possible route to understanding geometrical structures like the causal network like the multi-way causal network i should say because um one way of thinking about you know how does the say a causal space-time causal network limit or laurentian manifold or how does a hypergraph limit to a romanian manifold one way to think about that is kind of to flip the problem around and start from a romanian manifold or start from a lorenzian manifold and do one of these simplicial decompositions on it and see what combinatorial structure you get out and you you will get something that looks like a hypergraph or looks like a causal graph and um the the fact that this amplitude gives you a way of generalizing simplicial decompositions to these to these more abstract kinds of structures like you know like twister spaces and correspondent spaces and so on uh tells us that maybe there's something there that will give us insight into what the what the limiting geometry of things like multi-way causal networks uh is but um as you say that that has to be worked out in detail well so i mean what you're saying basically there is that when we say you know you take a picture of a i don't know a picture of a rabbit or something you can triangulate you know there's a classic you know the stanford bunny is the classic one where you have this three-dimensional object and you're taking the surface of that three-dimensional object and you're breaking it into lots of little triangles that's a triangulation of the space what you're saying is that if you have more abstract spaces in particular twister spaces and you want to do a decomposition of the twister space into polytopes generalized polyhedra you're saying that the amplitude dihedron is a way to think about that decomposition i i wasn't aware of that version of the of the amplitude ahead story i mean i was more aware of the story of the scattering amplitudes where i mean you know we really need to formulate scattering amplitudes properly in our models because basically a scattering amplitude is has to do with thinking about multiple paths and the multi-way graph and the story of what happens to those multiple paths see this is one of these cases where a scattering amplitude normally in quantum field theory what is the scattering amplitude the scattering amplitude is you take two particles at infinity they come in they collide they go out to infinity again and you ask the question what is the relationship between the particles coming in from infinity and particles that go out to infinity and that relationship is usually described in terms of the s matrix you basically take all the possible the vector of possible states of the incoming particles the vector of possible states of the outgoing particles and you say these are related by the s matrix so it's a very outer infinity but with particles and the question is can we get a version of this that doesn't require us to know how the particles work can we get an analog of that scattering aperture because in quantum field theory scattering amplitudes are talked about in terms of asymptotic particle states which by the way are a total can of worms to define and in quantum thermodynamics for example qcd theory of quarks and gluons it has been impossible to define those asymptotic states they just don't we don't know what structure they have because usually in the notion of asymptotic states is when particles are sufficiently far away from each other they don't interact with each other great that's all good and well and good until you realize that in a proton the quarks are permanently confined so you never get quarks to be far enough apart you can think of them as asymptotic and never interacting so um that's uh but but um you know i think so we don't really know and maybe we need to think harder about is there a version of the scattering amplitude story that does not rely on particles and i think what you're implying jonathan i don't understand it is that in terms of this decomposition into polytopes that somehow there's a version there's a way of getting something like but by the way the amplitude dihedron is a derivative sort of the string theory thinking that was a derivative of the old s matrix theory of strong interactions which basically said let us consider this s matrix what can we say about the s matrix oh it has certain properties it has unitarity it has analyticity it has crossing symmetry analyticity is is that that as a function of the parameters like the memento of the particles that come in there's a certain continuity with respect to changes in the momentum crossing symmetry is a more complicated thing that has to do with exchanging particles and anti-particles and so on but these are features of this thing that is the s matrix and we can kind of hone in on what the s matrix is by saying the s matrix is this mathematical object with certain features and um uh you know what the analog of that is between this sort of triangulation of a space and so i don't know maybe jonathan knows knows how that works well yeah again as like i said i i don't i don't really know and i understand enough of the underlying quantum field theory but so the the geometrical picture of what happens is apparently if you do the on-shell scattering processes you know that they form a tree of possible outcomes that's very much like a like a multi-way evolution graph and where the you know the scattering amplitudes are the individual sort of weightings of the in that tree and the the geometrical structure of that of of that on-shell uh uh scattering tree is a essentially a generalization of a complex polytope um which is which you can think of as in turn as being a generalization of a simplex in some you know some abstract projected space um and then but because the you know because that that's uh that positive cosmoline is then used in the computation of the of the scattering amplitudes it's then referred to as the sampler two here and it's some some generalized complex polytope that's used in the computation i think the hedren part of it has to do with the the um momentum conservation and i think that has to do with that basically to say you've got a bunch of vectors that all sum to zero is the statement that you're inside a polytope of a certain shape right right so i think that's the um and the on you know by on shellness it's just the story that the the p squareds the momentum squareds are equal to the mass squareds um and that's um uh anyway okay fair enough um [Music] question from talker about strong and weak nuclear forces that's kind of what we're talking about in terms of that things are invariant under a local gauge transformation that is su-3 cross su-2 cross u1 and su 3 and s2 and u1 those are designations of types of lead groups essentially symmetry groups of um of different kinds of things su 2 is is um is roughly the symmetry group the rotation group although it's a little bit more than the rotation group um su-3 is a as a generalized um uh um um well these are s u stands for special unitary that means that it is the set of matrices that have determinant one on a unitary matrices three by three unitary matrices with determinant one is the is a way to think about what's what's in that it's the group of those things but but i mean that's that's an obscure way to say it that's an obscure mathematical way to say it but basically that what's it is generally believed that this these three different pieces the su-3 is the thing that gives you the uh gluon sector su 2 cross u1 gives you electromagnetism and the weak forces um but uh it's generally believed that all those things actually are part of one sort of master group that breaks down into those three separate subgroups um and uh the question is in our models if we look at the limit just as we can look at the limit of a spatial hypergraph and say what's the limiting space time what's the limiting dimension of space or whatever else what's the limiting lead group the limiting continuous group that you get when you have a big enough kind of bag of permutations in our models and we don't know and we don't know whether there's particular families of lead groups that are possible to get like for example if we could show that everything you get would be have to be a subgroup of e8 for example exceptional group e8 um then that will be a spectacular thing to show because su 3 cross sc2 cross e1 is a sub week for su su5 which is a sub group of so 10 which is the subject of e7 to the subgroup of v8 if i remember my my lead group theory correctly um and uh to you know it's it's by no means obvious it's by that it's completely unclear but but it could be the case that there's a generic fact that the um uh that this structure this limiting structure has to be some subgroup of this particular kind of lead group i don't know if that's true if that was the case it would give us a tremendous boost in terms of thinking about the standard model of particle physics we don't know if that's right um questions here about particles of maximum entropy and so on that's a that's a big can of worms i mean entropy the notion of entropy is the notion of when you look at a system how many different microscopic states are consistent with what you what you describe how you describe the system so if the way you describe the system is to just say oh it's a big bucket of nodes and they're roughly arranged to be three-dimensional so that their average dimension is three then then that implies a certain entropy because there's a certain number of microscopic arrangements which are all compatible with that macroscopic statement um and uh you know how that works in terms of different regions you know how what entropy you assign depends on what your microscopic description is in the in the language of um like gibbs and people like that the the sort of theoretical statistical mechanics it's the course graining procedure that you use which determines the effective entropy that you will get and people have sort of naively just barreled forward with certain assumptions typically from chemistry about what the course training preserve and from from uh sort of uh practical thermodynamics and for for engineering with what the appropriate course grading procedures are it's not clear how those relate to what the sort of theoretical ones could be um but uh um yeah so that's a complicated story um how many generations we have to go in the evolution of our models before we start to see particles we don't know but in our in our current estimates it's really a lot like 10 to the 80th and things um which is you know far too many for us to simulate and we have to hope that there's a way of kind of mathematically jumping ahead and we've been surprised how successful we've been able to do that um let's see question here from ryan uh why do most modern scientists use math to validate their theories but claim that math is also man-made shouldn't math be fundamental like a scientist in a video game using code but denying that the code exists oh boy that's a complicated philosophical tangle there um the uh ah gosh and i might be the right person to ask this question because i really thought about a lot of the pieces that go into this i mean the you know in our models it's just it's a model that says you apply these rules and if you apply them enough times you get something which is uh which is in precise detail what our universe is like it doesn't say it is our universe because it's an abstract set of rules it is a representation of our universe now if you say if we are entities within that universe operating according to that representation of the universe how do we think about using the representation to represent the thing that is being represented by that representation um i it actually i don't think is that difficult it's it's a it's basically just saying that there is a you know there's a representation which okay the real issue is in our brains which is what we care about because that's where we're thinking about stuff can we make a bridge between what we can understand in our brains and how the actual universe works and can we make a representation of how the actual universe works that is accessible to our brains and that's kind of what the story of actually explicitly creating models is about otherwise just say why bother to create models just say here's the universe it just does what it does be happy so to speak so i mean there's there's probably more to say to unpack this better but that's my that's my immediate um sort of real-time philosophy version of that uh okay question from jay low here is there an interpretation of the speed at which time is ticking is it possible that time speeds up with the growth of the hypograph yeah so in our models time is the inexorable progress of computation so time is only we only perceive time insofar as time in us is going forward that is if if nothing was changing in our brains we wouldn't perceive anything as happening we have to our brains have to be updated just like the rest of the universe has to be updated but but our brains have to be updated for us to perceive the changes in the rest of the universe so time is in our models simply this inexorable process of computation by which things are updated and so psychological time is the updating of things in our brains astronomical time is the updating of the structure of the universe and so on and all these different arrows of time are necessarily aligned because they're all just about the progress of computation and this question of his time speeding up is really sort of a meaningless question because it's time is defined by that inexorable process of computation it's happening in our brains it's happening in the universe at large the it's it's sort of happening everywhere at whatever rate you say it's happening because you could just say oh i don't want to consider the next update in the universe i'm just going to take the universe as it is now and not consider the next one but the next one will happen in the universe and if you say let's see what consequences that had for our brains you will conclude that the next step of time occurred so there's no sense in other words we're all sort of locked together us and the universe are sort of locked together in the perception of how fast time goes now we can have things like we could sort of reach a singularity we could reach the point where the universe just stops but we won't perceive that because we will have stopped and so it's just like it's the end you know game over so to speak but it's not like we would ponder oh my gosh that's so unfortunate the game is over we just stop and there's no more pondering to be done everything is finished um i don't think that's the way the universe is going to end but that is something that can happen in parts of the universe like inside black holes so question is are we worried that our set of tools won't be enough to understand the fundamental nature of reality oh yeah i mean you know i don't know whether how far we're going to be able to get you know this year this decade this century we don't know we simply don't know we've gotten a lot further than i expected we've gotten further than i thought we'd get in a century so that's very encouraging but you know it doesn't mean that we don't know how far we'll get how quickly and what level of tools will be needed to understand what kinds of things um as i say it's been going better than expected that's all i could really say question from mega is can there be a region of the universe where time runs a hundred times faster um you know i kind of partly answered this but but time is also related to energy in our models and um in a sense one could say that there is um if you imagine so and again this is the time running faster is also related to causal graphs and relativity and so on i mean that's a that's a complicated mess of a question um in the sense that uh you know just like in a gravitational field there is the time effectively runs faster yeah it's a complicated a complicated question i mean i think that um and you have all kinds of twin paradoxes and so on i mean the answer is yes time can run at different speeds in different places because time is something which is a is part of the dynamics of our brains operating and that dynamics is affected by the overall dynamics of of the of the structure of space and and what's happening in the universe at a particular place in the universe uh there's a question from joe uh is particle physics time reversible does that imply the rewrite rules for the universe must be symmetric um uh two points first of all even if the rules are not symmetrical on average after you run them a lot of times they will behave as if they're roughly symmetrical if they if they don't as soon as you get some kind of equilibrium where the sort of on average things more or less stay the same that implies that running it forwards in time and running it backwards in times will look roughly the same that's that's the first statement to make so it's unremarkable that there is approximate time symmetry in the in the universe there isn't exact time symmetry in the universe the universe is expanding and that generates time asymmetry in all features of the universe if we look at them sufficiently closely now there's another phenomenon in particle physics which is quite separate or so it appears from the expansion of the universe that's the violation of time reversal and variance or cp violation charge congregation parity violation um it's a phenomenon was discovered in 1964 uh somewhat surprising phenomenon that was initially observed in the obscure decays of the k0 meson i mean obscurely what happens is that the k0 particle particular kind of short-lived particle lives about 10-8 seconds 10-8 and minus 10 seconds um the uh for the k0 um it is a particle which decays after 10 to the minus 10 seconds on average into two pions okay or sometimes three pions but um the question of whether ah this is this is going into quantum into details of quantum mechanics but there are for people who know quantum mechanics there are two eigenstates so that k zero and k zero bar the k zero particle and the anti-particle with k zero the the eigen states the quantum eigenstates are combinations linear combinations of the particle and the anti-particle anyway blah blah blah long story but basically what happens is you can see fluctuations between the the um the k zero and the k zero bar in um uh in the evolution of such a system and what you would get going forwards in time the fluctuations look different from the ones going backwards in time and so that's a kind of way of seeing time reversal violation uh that that the universe's microscopic laws are not time reversal invariant but that that doesn't mean that for example probability isn't conserved that's perfectly well conserved it just means there's a detail of the way the universe works that for which the time is not symmetric whether that is connected to the expansion universe nobody knows um i doubt that it is actually i think it's probably a different phenomenon but we don't know how that works in our models we have some vague ideas of how [Music] well we have some vague ideas but we don't know in any detail um let's see it's a question from joran here is the possibility no tiling pattern creates space the locality arises purely from the fundamental rule doing some sort of graph simplification yeah yeah that's that's that's more or less the story the spaces space is not in our models any kind of regular grid or tiling space is this complicated mess of connections between these these points in these graphs and it is the fact that there is a large scale structure that on a large scale the graph has certain properties that leads to the fact that space appears to have the kind of continuous simple continuous properties that it does um okay there's a question from winter storm how are hypographs in our system related to hypergraphs that neural net researchers use or causal studies at the perimeter institute wow okay i think those are two really different things so i'm guessing causal studies is probably causal set theory and i think jonathan is even as we speak writing a paper about the detailed connections between causal set theory and our models causal set theory is kind of a a simplified special case of what we're doing our models provide kind of a a um a dynamics for causal set theory um and uh uh jonathan do you want to make a more specific comment there uh not really no i think that yeah that's pretty much exactly exactly what the correspondence is at a high level so um so our model is kind of one way you can think of it is it's an algorithmic procedure for generating causal sets deterministically so causal set theorists generally how they've thought about these things as they as we kind of discussed earlier um you you know you start from some space time you start from some lorenzian manifold and then using something like a poisson process or something some uniform sampling process you you sprinkle uh space-time events uh in such a way and then and then you define a causal partial order between them that's consistent with the underlying causal partial order of the space time and so you get this discrete approximation to the to the space time which is the causal set um and then there has been more recent work uh relating to these so-called classical sequential growth models uh developed by people like david writeout which which attempt to define a dynamics for causal sets by kind of uh essentially in a stochastic way and um so a few points to make so so what one is yeah as i said effectively our approach with causal networks basically if you take a transitive reduction of a causal network you get a causal set you get you get a hassle diagram for a causal set um and so they are just algorithmic procedures for generating causal sets um these kinds of dynamics that people have considered in causal set theory like classical sequential growth they are special cases of multi-way evolution so so for instance the classical sequential growth model is the model in which there is no isomorphism testing so so every uh all you just get divergences in the multi-way evolution graph and in which at each step a single uh node is being added as so you know a single space-time event is being added at each step and and it so if you evolve the multi-wave graph of you know for such a system and you assign each each path to it to have a sort of uniform probability what you recover is exactly the classical sequential growth model of causal set theory um there are also other kind of correspondences which are which we're also sort of studying so for instance this approach to solving so formulating the einstein field equation sorry in causal set theory using this thing called the beninca delca action which is kind of the the discrete analog of the einstein hilbert action it turns out that's a special case so we have a way of formulating einstein hilbert action a discrete version of it that depends only on the assumption that the causal network dynamics are are weakly ergodic that they satisfy basically some molecular chaos assumption the benign casa dauca action assumes that they are that the the causal elements are produced by this poisson process so the poisson process is a particular instance of a weakly ergodic dynamics uh but but it's not the most general case in effect what we have is a is a significant generalization of the benincasa dalca action in our formulation of the einstein field equations so in a few different places we can see where causal set theory basically gives us uh certain idealizations to or certain uh special cases of the things that we've been investigating in the context of our models roughly one way to say it is we have a dynamics that actually generates according to a rule certain things in causal set theory we just say let's pick at random these things and those things that are picked at random are roughly something that could be generated by our kind of model that's that's i mean you know they're just by fiat you're saying you pick things at random and cause all that theory but whereas we're saying we actually know how to generate those things um okay let's see the second part of this question was about um uh neural nets and hypergraphs so usually in in neural networks one is dealing with ordinary graphs hypergraphs have not really been a thing yet in neural nets except that we were just looking at the generalization of our um neural net framework in wolfram language and actually just starting to look at some hypograph generalizations of that um so there are uh the the the way that graphs arise in um a neuron that's a little bit different or it's it seems that way at least um because neural nets tend to be organized in in things like particular layers and so on and it's it's sort of a well it appears to be a different story from the things that we're dealing with at least for for the time being although maybe there are some analogies between the way that training works in neural networks and the way that multi-way graphs work in our systems but i don't yet know that um question from uh saints does the atomization of space provide a solution for the navy stokes equations no the navier-stokes equations are um okay there are a couple of things to say about this the navier stokes equations are the equations of fluid flow and one of the things about fluid flow is fluids are ultimately made of molecules when people try and solve the navier-stokes equations on a computer they end up having to break down the continuous fluid into discrete pieces and then see how to uh take limits as those discrete pieces get small in a real fluid it's sort of taking that limit physically because it has discrete molecules and you're just seeing a large number of discrete molecules doing their thing i mean i made up this method for doing fluid dynamics back in the mid 1980s that was based on just starting from those discrete molecules actually very idealized discrete molecules and then building up to the full navier-stokes equations you can think of our approach to the um uh to the einstein equations being sort of the analog of that but instead of dealing with uh with these sort of discrete molecules in a fluid we're just dealing with these this sort of discrete atoms of space and so on and so there's a notion in which what we're saying is we could work up to the einstein equations from these discrete uh structures of space time rather than working down from the einstein equations and and making discrete numerical approximations same with the navier-stokes equations now the question in the einstein equations is uh you know what singularities are there in the einstein equations what bizarre things can happen in the einstein equations and going down from the continuous version of the einstein equations people have been able to figure out certain things we are learning different things going up from the discrete version of the einstein equations and so for example that faster than light analysis that i did recently is a is a creature of going up from the discrete end rather than down from the continuous end now in the case of the navy stokes equations there's a question of what things can you learn going down from the continuous and up from the discrete both are difficult really difficult so for example the big issue with the navi stokes equations is existence in uniqueness that means given the navier-stokes equations given these mathematical equations is there uh well is there a unique fluid flow consistent with saying the fluid has starts in this with this velocity and has this boundary etc etc etc is there a unique flow for the fluid consistent with that or more bizarrely does there exist a fluid flow what on earth does that mean well that could mean you think you can set up the equations with these initial conditions but after a while the equations say sorry there's no solution now you can say but but look how could that possibly be right because the physics has to do something the fluid has to do something what does it mean that the solution doesn't exist okay it's a complicated thing one of the more amusing cases of that or amusing i don't know but but interesting cases of that when people were trying to uh first break the sound barrier with planes there are these bizarre instabilities that happen near the sound barrier and those can be thought of in terms of the equations people studied at the time as what happened you know when the solution to the equations doesn't exist that's the that's the time when you're when your plane undergoes these huge you know instabilities and and you know the thing is almost pulled apart and so on or actually was pulled apart unfortunately in a bunch of cases when people first tried to do that but um uh the the um so you know uh the question of existence and uniqueness for the navy stokes equations which is sort of a key problem there is a question of when you go down from this continuous formulation what you get to um uh sort of those questions don't exist when you go up from the molecular case but you might what what well they do exist in the following sense it could be the case that when you go up from a like molecular level you simply never reach something which can be described in terms of continuum equations and that's the situation that we're talking about in the einstein equations and in in in structure of space-time it could be the case that there are these bizarre features of space time which come up from the discrete and you never really can identify them as being a thing in the continuous space so an example of that is topology change if you want if you have something that consists of a um oh i don't know it's a sphere and then oops it turns into a donut with a hole in it that's not something that can happen in a continuously in a continuous system but it can happen in a discrete system and so there are things like that that a possible phenomena that just could exist coming up from the discrete and don't exist going down from the continuous and there might be phenomena like that that exist in the navistox equations i'm not sure there might be things associated with turbulence which we don't know whether turbulence is a phenomenon of the continuous navier-stokes equations or it's a phenomenon that relies on details of the molecular structure of the of the fluid to explain why there's all this randomness i personally think it's probably properties of the continuous equations although we super hard to find there actually i found some toy versions of those equations 25 years ago or something that uh a student from as uh working with us is studying right now that um have a bunch of these properties that are a bit like the navi stokes equations in having in producing really random complicated stuff even though they're very simple equations and even though there is in the case of those equations there is no underneath to those equations there's no molecules that made those equations they're just mathematical equations that you write down ah let's see it's a question from andrew here in our models does entanglement have a limit in physical space well let's see um that depends on the relationship between branch shield space and physical space and local multi-way systems and so on and the answer is probably yes but we don't completely understand how that works yet i think and jonathan has disappeared from video and may have disappeared completely but he might have an opinion on that subject no no sorry i i left for a moment um yeah so basically what that's asking is i i think what this question is asking is is the maximum entanglement speed implied by our model can you know can you ever get to a point where that provides a you know sufficient impediment that you can no longer entangle two microstates if they are uh you know separated by a certain distance in physical space so so just like in uh in cosmology in in ordinary physical space we have things like the particle horizon which tell us effectively the the the outermost limits of the things that we can ever be causally connected with in space time uh i guess the question is asking is there an analog of the particle horizon but for entanglement the answer is yes my reasoning yeah and the answer should be yes it would be much much larger probably than the actual than the cosmological particle horizon but it will presumably still be finite how it compares to the actual cosmological size of the universe that's an interesting question we don't and i don't think also in the case of black hole mergers we don't know you know the speed of light limits the speed at which black holes can merge but the maximum entanglement speed also limits the speed at which black holes can merge and probably for small black holes the speed of light is a more important limit for large black holes it's not so clear you know it depends on the scale of the entangled maximum entanglement speed but what you will see there is an actual physical effect of you know entanglement will be the limiting feature of you know to get these two black holes together there will be a limit to how fast the quantum states can be entangled but we don't you know we don't yet know the precise dynamics of how that works right uh there's a question here from mustafa when does energy become a particle in the hypergraph well so we have a bulk notion of energy and the question of how and every you could break down that energy you could kind of decompose that energy probably into these things that we can think of as being like particles we don't yet know how to do that um but in general the sort of bulk presence of energy can be thought of as the as the sum of lots of microscopic particles that each have a certain contribution to the energy and that's um um and that's the um but if you're asking when does energy become like a particle that's kind of a um there is no notion of well in standard quantum field theory all energy is thought of as decomposed into particle excitations whether it's a photon that's more sort of pure energy or an electron whatever in quantum field theory one of the ideas is all energy is decomposed into particle modes now i say all energy and there is a little bit of an exception to that because there are these um uh other solutions like instant on solutions things like this that are kind of other so-called non-perturbative solutions to the equations of quantum field theory that um are not just like particles but most of the time in ordinary in in things which we think of are directly connected to experiments we where we're doing scattering experiments and things we always say we're going to start with particles and end with particles um and so in those cases the um uh the notion that the idea is all energy can be decomposed into particles um that's what i thought we were going to have to understand to understand energy in our models we actually have a bulk version of energy where we haven't decomposed it yet into particles but presumably our energy can be decomposed into particles as it comes in canon quantum field theory except maybe the cases where it can't be except maybe there are cases where there are structures that aren't like particles like in quantum field theory uh well in in you know there can be things like cosmic strings that aren't really like particles or ordinary strings that aren't really quite like particles although they have certain similar features other kinds of sort of collective structures that aren't really like particles we don't know how those work yet in our models by the way i i should mention i have a suspicion that there may be a sort of ramsey theoretical way of viewing that that in other words when you have a sufficiently large number of causal edges certain topological obstructions essentially become inevitable um so that if you're only looking at a small bundle you that there is no obvious sort of decomposition into particles but as soon as you have a sufficiently large ensemble of causal edges it will naturally decompose into particles essentially for ramsay theoretical reasons that would be an interesting claim let me see if i believe that claim i have no idea if it's true it's just it's a suspicion that i've had well i mean so the you know to comment for people about ramsey theory the point is that in a sufficiently large graph for example there inevitably have to be just by the by the nature of the graph there inevitably have to be certain features that actually let's take a simpler example in any in a sufficiently long sequence of numbers you eventually have to have numbers that form an arithmetic progression i think that's a correct ramsey theoretical result um and that's to say well if you have enough numbers there's just no choice but to have a things that are in arithmetic progression you're not saying which arithmetic progression but there exists some arithmetic progression and there's similar statements about graphs what jonathan is suggesting is that it's an interesting possible idea it would have to generalize ramsey theory quite a bit um probably but it would be in the same sort of spirit that i i don't know it started off with the conjecture about um i was thinking a bit about cosmological bariogenesis and whether there's a whether there's a ramsay theoretical way of thinking about that right that once the once the hypergraph reaches a certain size certain features of certain topological features become certain topological obstructions become inevitable and i'm also wondering whether there's there's an equivalent thing about it you know if you if you have sufficient energy density if you have sufficient causal edges if there's enough hypograph activity uh yeah that again certain topological features become inevitable it's it's a generalization of ramsey theory in the sense that it's dynamic in a way that ramsey theory generally isn't right so we should investigate this this is another thing to put pin on the on the uh on the list because we can investigate this completely empirically and that's a good thing to investigate yeah i agree that that's a i mean in other words what subgraphs for instance are inevitable subgraphs that have to occur that would be a concrete way to investigate this um we're probably running out of time soon but um let's see the question from permanente is about the compactness property of logic i don't know what the compactness property of logic is does jonathan know yeah so so there's um okay so quick quick quick background to why it's called the compactness properties there are these things called stone spacers which are these totally just these totally disconnected uh household spaces in topology um but they're but crucially they're they're compact spaces and it turns that they were studied by this guy stone uh for amongst other reasons the fact that they turn out to be a natural kind of topological interpretation of boolean algebras boolean algebras have a natural spatial structure and it's the it turns out it's these stone spaces there's a there's a theoretical structure it's a hypergraphs right i mean it's it's true to the n-dimensional hypographs isn't it basically i'm sorry hypercubes i meant to say hypercubes yes right exactly that yeah if you formulate them as a lattice that yeah they they form they form hypercubes um and so then in topology there's the thing there's this thing called tikkanov's theorem uh that says if you take a if you take a the product space of a bunch of compact spaces and that product spaces itself compact so if you apply that to stone spaces corresponding to boolean algebras it tells you something about about first order logic and in particular it tells you that if you have a say if you have a collection of sentences in first order logic then that set of sentences will have a model if and only if every subset of it every subset of those sentences has a model um which is basically what you're doing is you're taking your stone space which is compact and you're you're looking at the subspaces and showing that those are also compact um in terms of how you interpret that in our formalism uh i have a conjectural answer but it's not very well thought through uh because i'm literally just thinking about it now but the but okay so i love the way you say hello conjectural answer because you thought of it right now okay keep going right because so interpreting these multi-evolution graphs as being proof graphs right um so so your your multi-way rules correspond basically to axiomatic transformations between symbolic expressions each node is a symbolic expression every path in the multi-wave evolution graph is then a proof of equivalence between some expressions or proof of implication between expressions um so then in that instance we have this again this sort of conjectural way of formulating models by coordinating those proof graphs effectively by foliating them into you know into in sort of expression like hypersurfaces or whatever the appropriate name is um and so so each each such choice of foliation is a different choice of model and so essentially what what the if that's if you consider multiple systems that are produced by first order theories what the compactness theorem would be telling you is that so we already know that if you have you know two multi-way systems corresponding to individual rules you can consider the composite multi-way system which is like some kind of tensor product of the two individual multi-way systems uh and so what this would be and that actually has a natural product topology which is already quite encouraging and um so what this what the compactness theorem basically be saying is that the is that your uh composite multi-way system is foliatable if and only if all of the sort of constituent multi-way systems are foliatable which is an interesting thought and not one that i'd really sort of internalized so so what that would mean is to be foliatable is to say there exists a model yes right and so so we exactly so and and we know that there are certain combinatorial properties that have to be satisfied for the system to be foliatable so one example is there can't exist cycles uh if there exists cycles that's a that's a failure of hyperbolicity uh in the in the continuous interpretation of the of cycles in a meta-mathematical graph that is an interesting well i i i guess it's a that's some kind of tautology right that's or that some that's some circular some inevitable circular reasoning i don't know well it's saying that that is you apply the axioms basically it's telling you that the deduction relation is not well founded which is another way of saying that it's circular which is probably to say that almost anything is true in some sense that you that you will get back to why is it wait a minute no there's there's more to this if you have something where you apply the axons you play the axioms they go through a bunch of different states and then they come back to the same thing again in the usual interpretation i think that means that that some reason i think that means that anything can be considered true that there's some that that you don't connect to a truth at the top so to speak that implies a bunch of things you're independently yeah okay so but but that's an example yeah we we need to understand closed timeline like curves in mathematics so okay another another thing pinned to the the list of things to understand all right um that was an interesting question though thank you um uh confused is asking in a computational universe is everything running at the same speed is our time just a human perception of the speed of computation in in in branch of space yeah i mean yes time is the everything is i was as i was explaining before i mean it's like our brains are computing our um and our um and the universe's computing and the sort of rate of computation the intrinsic rate of computation is can be considered to be the same you could consider it to be different you could say our brain didn't update at all but then we have no we have no perception of what happened in the universe so you might might as well say it's all happening at the same at the same speed uh okay so let's see torrey is asking returning to the neural net theme adversarial attacks seem to point towards a much different way that neural nets perceive data and change a picture just by changing a few pixels and so on so we're trying to make them think with our prior but they still do something different right so the question is how do you confuse a neural network versus how do you confuse a human uh you know us we think that the confusion of us humans is less fragile than the confusion of current neural nets and that's probably true and that but that probably has a consequence of some details of the way that your current neural nets are trained and so on i doubt that i mean you can confuse humans in all sorts of ways it's like you know you ask a person why were you confused and in the end there'll be a very complicated story often of why they were confused i mean it's like why do i think you know i glance at something and i think oh there's a you know there's a there's an eagle in that tree but actually it isn't an eagle actually it's a pattern of leaves and it's like well why was i confused and um you know it's complicated and i don't think that my story of confusion is necessarily any more embarrassing so to speak than the story of confusion or less embarrassing than the story of confusion of a neural net so i i don't think there's a fundamental difference there i'm not sure but i don't think there is and i think that the the notion i mean the common thing with humans is we get to use common sense from other places to think about things whereas our neural nets tend to be um you know one trick ponies so to speak that are just doing one thing and don't get to you know if the neural net concluded that is a picture of a crocodile riding a bicycle right based on its way of understanding how things worked and you say but crocodiles don't ride bicycles that's just not the way bicycles are set up but that's a piece of knowledge that in principle could be part of what the neural net knows but isn't what the one trick pony of an image identification neural net is supposed to do uh richard here is is asking given a rule set that exhibits universal computation uh one may nest wolf and model inside itself might we discover such matter interpreters in the natural universe what would this imply yeah i think such matter interpreters exist all over the natural universe i think universal computation is ubiquitous in the natural world and what that implies is tons of computational equivalence that is we look at something and we say we're very smart we can figure out what this thing does but no that's not the case because it is as sophisticated as a computer as our brains are and so when we look at this thing it's like it's just equivalent to what our brains are doing so we don't get to figure out what it does any more than than because it's just running a computation that's equivalent to what we can do in our brains so i think that's the the sense in which the existence of embedded universal computers embedded within the universal computer that's the story of what cannot be predicted is is things that for which brains aren't out ahead brains being an example of universal computer but lots of other things also being examples of that um question from nordarico what has been the most interesting or valid disagreement regarding our work from from other physicists oh boy you know the most interesting thing is that a bunch of physicists i know who are good physicists uh have been seriously trying to understand what we're doing and they have a hard time because they have a certain way of thinking about things and this is different and you know i think we are realizing that you know these bridges like the one that jonathan is working on right now to causal set theory are you know we probably have to build a lot of these bridges now a bunch of people particularly younger physicists um who are working on our our uh models um you know they've learned they've learnt the stack of knowledge that we have in our models and and that that relate to our models and that's allowed them to to contribute there and i'm afraid i've been a little disappointed actually that people have been less interested in making connections to all these other wonderful areas of physics because like well we're making a lot of progress on these models let's just keep going why should we worry about how these relate to string theory we don't need string theory right now which i think is a shame because i think it's actually not true i think string theory has gotten a lot to say that will be very useful to us and vice versa but in terms of of um i don't know i mean they've been people um some number of people don't understand how lorenzen variance works in our models and i'm confused by this is something that i accuse jonathan of saying i'm confused why you're confused um and um this is um but but you know to be fair any time when people you know try hard and they're still confused it's a you know look i've spent my life uh producing you know software and computational languages and so on and you know to me i take user confusion personally so to speak in other words if a user of our system is confused then it isn't the user's problem it's my problem so to speak and we didn't explain it properly or it's badly designed or whatever else and i think to some extent we we still need to do more work to really uh explain uh you know in a way that is unconfusable so to speak how some of this stuff works and one of the issues is so you know we can explain it at an intuitive level works well we can explain it at a mathematical level works well the mathematical level is kind of sophisticated in some ways and the question is you know at what level by what vector do you want to understand something and that's that's you know that's a challenge for different people because people different people have different i mean for me you know i like to break things down and in terms of things that are for me simple but you know for me simple if it involves some random factoid of quantum field theory that i happened to learn when i was 12 years old for me that seems simple but that's not necessarily simple for somebody else and so you know i think it's a question of of um uh of you know how do we how do we make these bridges to different places but i don't think you know at this point i i don't think we've encountered any this is a terrible thing to say but i don't think we've encountered any interesting sort of oh how can this possibly be true type type thing i am am i am i mistaking something jonathan i mean we've we've encountered i don't understand this you know i you know it's like like i don't understand it you know put it in my context type thing but i don't think we've encountered um you mentioned the lorenzen variance thing which i think is actually a good example because so i i've i had this long exchange sort of a little while ago and i've it's just restarted again with a fairly famous physicist who i won't name in case they don't want to be named but uh who was particularly interested in how we how we get around this problem of lorenz invariants and uh yeah so we get around a problem of lonesome events she thinks that that we have a a at least i assume she thinks that that um um we have a um uh that a model of our general type couldn't possibly have lorenzen variants well it's it's a good it's a good point right that in some sense that um it's very counterintuitive well okay at least it's counterintuitive to me the idea that you can have a discrete model that is compatible with a continuous symmetry group right the lorenz group is a continuous group and so i think most people have come to this with the geometrical intuition that a discrete space can't be invariant under under a continuous group but that's ridiculous because if you just have a grid right if the limit of a grid is invariant you know well at least a randomized you know a random walk a discrete random walk is invariant under rotations right a grid is a good example of something that is not invariant of rotations right because that's grid is something where you can pick out a preferred direction and so for a random walk you cannot right right but so you know in in causal set theory uh you know the way the way people deal with this is that there's this uh actually quite elegant uh measure theoretical argument that's due to bombelli uh which works by saying you can't define a you can't define an equivariant measurable map which will be used to pick out a preferred frame because essentially because the hyperboloid of your units uh future future directed time like null vectors um is uh is is a non-compact manifold um and so you so if you could pick out a preferred frame you could basically use it to make your measures arbitrarily large um which would violate the axioms of a probability space whereas in euclidean space you you can pick out a preferred frame uh because the associated the the the space of um of unit vectors in euclidean spaces is like you know is sn or sn minus one strictly speaking which is a compact space and therefore that argument doesn't hold um but in our setup with causal and variance actually there's there's a subtle difference and actually um this is related to the thing i'm currently writing up for this causal set paper is exactly how this this uh this argument changes in our in our setup so um you know cause and variance the statement that the causal network is is always the same you know it's always isomorphic for different updating orders um the the different choices of updating orders correspond exactly to different uh conformal corresponding exactly to the conformal transformations of space-time so so the the transformations between different reference frames correspond exactly to the actions of the conformal group and so because both the lorentz and pancari groups are subgroups of the conformal group uh you know calls and variants necessarily implies lorenzen variants in the continuum limit as as a as a sort of um as a corollary um but the the place where i thought this particular uh discussion was interesting was because the physicist i was i was talking to um sort of accepted all of that but was saying nevertheless it has to be the case that the out degree of your of your individual updating events in the causal network has to has to be infinite and again if you follow through the argument naively that does in fact seem to be the case that the that um again because of the non-compact nature of this hyperboloid uh and because all of your future events lie in between the future light cone and the hyperboloid um it appears as though the number of immediately events immediately in the future has to be infinite so the out degree has to be infinity the subtlety there okay there are several problems with that um one one of which is is assuming particular features of the of the distribution which in fact we don't assume but actually even if you assumed something like a poisson distribution it's still not quite right because you're assuming that the individual causal edges are in our actually observable quantities yeah your toast once you have a poisson distribution you've just you know you've just determined your space time basically by by saying what the measure of the poisson distribution you know poisson process is right right but but even in that case it's still recoverable um so and this is again one of the things i'm trying to write i'm surprised it's recoverable in that case but okay well it's recoverable as long as you would basically impose a cutoff on your boosts if you say i'm allowed to boost up to like 0.99 c then what you can do is say because our causal edges are so much smaller than anything that can even in principle be observed what you basically yeah it's buying an effective theory in which uh so actually i can just quickly share the draft of the paper um you can define this effective theory so here's your causal network but this is not itself actually observable the things you're observing are big you know blocks of of updating events and big blocks of course ledges so you're basically defining an equivalence relation which is shown here so we're by we're partitioning this causal network into equivalence classes that are here shown in red yellow purple etc so the effective causal network you're seeing is this and so of course by making those equivalence classes arbitrarily large you can force the out degrees of the of the vertices to be arbitrarily large and so effectively as long as you're okay with the idea that you're enforcing a cut off on the maximum boost the space you end with this still causal invariant and and that's a that's a kind of a subtlety that i probably i probably wouldn't have picked up on unless i'd had this particular exchange with this particular physicist so i think that that's at least one example of something which helps clarify my own thinking about this oh yeah i mean look for for me for us like these discussions and you guys asking these questions on this live stream this is highly useful if you you know uh hopefully we're you know providing something interesting for you guys but but you you are providing something very useful for us um even if all you do is ask questions and don't make any suggestions it's still super useful um because the the um but by the way i think the thing that i'm realizing is that a big part of what these guys probably don't understand is the the role of essentially molecular chaos in the construction of space-time they're still imagining that it's some kind of grid type thing um but yeah we you know we gotta we got to get some more um uh i mean you know there are a number of people in it i i feel bad about it because it's like they're really making an effort to understand and they're running into various problems like you know which include problems where i couldn't even see that the problem was there because it's like it's you know just my way of thinking about things is such that it just i can't see why there's a problem and um this is so so um you know but i'm trying to avoid jonathan's i'm confused about how you can be confused um the uh okay um ah richard is saying i better work quicker on the vr or model stuff i'm working on please please work on the vr stuff we really i really want to see this stuff in virtual reality and we we can we can get you um the the stuff that um that max has been doing i was showing earlier with them with those animations that's um uh those animations come you know they are they are minutes of cpu time to generate they are not the um the real-time spring stuff which we have uh which we have pieces of and and hopefully you've had we have some code which we're happy to share which has sort of pieces of implementing that in unity and so on does the model steven is asking does the model describe absorption emission spectral lines uh well yes eventually i mean it describes the features of quantum mechanics that will lead to a more absorption emission lines although it doesn't directly deal with those yet i think we're running out of time so i'm just going to skip forwards here and look at um look at other things here it's a question here from david about a particular explanation for the pioneer anomaly and i have no comment on that because i don't know what that explanation is and i'm also not even sure what the status of the pioneer anomaly actually is these days um i have to i'd have to look that up i i thought i had heard things about how oh no actually it's all been explained but i don't know so i have nothing to say about that um the question from uh json here do we lose our reference frame inside a black hole oh boy that's a complicated mess um how to describe that i mean when you go into a black hole the whole structure of space-time is is changed so it's not it it's there isn't really a you know the there are reference frames you can make but they're incompatible with the ones that we currently have and that's a that's a the one way of understanding what an event horizon is and we should mention by the way that that black hole singularities are an example of the failure of global hyperbolicity of space time so you know round of singularity a singularity is a point where if you attempted to foliate your space time you the the universal time function that you're defining would have level surfaces that all kind of stack up around the singularity and since one of the you know one of the basically the the definition of global hyperbolicity of space time is that the level surfaces are non-intersecting a singularity is a is a an isolatable point where you cannot foliate and which therefore a reference frame doesn't doesn't strictly exist okay that's uh i mean the definition that you're making of a reference frame is something where you have a a a reference frame something where you can sit there and time passes and things happen in the world is that a and so you're saying as a singularity time doesn't pass yeah pretty much right so yeah so the the well a formal definition of what a reference frame is is it's a rule for assigning points in space time to uh to to have you know global time values um and and so then the the space like hyper surfaces are the level surfaces of that function right um but yeah exactly for this reason because time doesn't extend because you know singularity is a point where your time-like vectors become inextended your time-like paths become future and extendable that's a point where it's not possible to construct that function because because the level surfaces necessarily intersect around that singularity the question here um let's see from matt our points on the hyper golf actual points that are connected via hyper edges or the points just the place at which the hyper edges diverge and converge i mean these things are just a representation of what's going on so so in the way we're usually setting it up the points in the hypergraph are actual points that are connected by hyperedges but there is a different view of what's going on where you start from the causal graph and you slice it and then you have a dual of that there are a bunch of different interpretations but but at least in the most direct interpretation there are atoms of space and they are connected by hyper edges um but but that's not the only possible interpretation of what's going on uh from christian here what drives the computation process that we perceive as time uh well you can be very paradoxical about this and you can say nothing drives it but insofar as it happens therefore we perceive it and we perceive time to have happened but from the outside the kind of uh you know the the um the external view of the universe which we don't believe we could ever get but if we could get an external view of the universe somebody could say wait a minute they waited a century to do that next update and um you know how can they you know but we wouldn't know that because we're embedded in this universe and so all we know is that the update happened so it's not a question of when did the update happen this is the question did it happen because the progress of time is defined by these updates happening and so there is no notion of the speed at which that happens um and and that's no notion in a sense of driving that computation process because if it doesn't happen then nothing happens and we don't know nothing happens because we don't know anything because we our process of perception is tied into something happening uh have we used machine letteris have you used machine learning for making progress and understanding things i use machine learning a bunch for doing automated i was looking for particular features of rules for these models and um uh doing sort of visual inspection of large numbers of rules and i use machine learning to filter that visual inspection so that's a place where we have used it we don't think we've used it for anything oh yeah i mean we we were thinking of using it for um basically lemma selection for trying to find paths and these theorem proving things but i think we may have a a better scheme that jonathan's come up with that is a physics-based scheme for doing that that that won't won't be a machine learning based idea um question from martian is traveling through branch of space like traveling through a wormhole not not really a wormhole is a different wormhole is a is a connection between two things where where space is like oh it's like a grid or something but then there's just this one sort of space tunnel there's this one extra thread that connects one part of the grid to another part of the grid that's more like a wormhole i actually talked about this a bunch in the post that i wrote recently about faster than light about things going faster than light i tried to talk about how how wormholes relate and so on by the way i think you you may be being a little uh overly dismissive of that question i mean that question is basically asking whether er equals epr is true right because you know a wormhole is some you know it is basically is a shortcut through a causal network is it a piece of the causal network that's not part of the continuum lawrencium structure a quantum entanglement is essentially a shortcut through branchial space it's part of it's a you know path through branchial space that's not part of the not part of the continuum geometrical structure and er equals epr is is making the is sort of conjecturally making the claim that the two things are related and i think that's kind of what this question is is okay that's that's okay i'm sorry i jumped too quickly there and i you might be but but let me just uh challenge the point about an entanglement being a non i mean in what sense the structure of branchial space is determined by micro entanglements so in what sense in the same way that's you can think of space the structure of space-time is being determined by microsoft okay so you're saying a long-range entanglement is like a wormhole that's a good point actually that's a very good point so you're saying a wormhole in space is like a long-range entanglement in bronze hill space right exactly so in both cases there that they're features that you've engineered in order to you know ensure greater correlation between two points than would otherwise have happened naturally it's just that one is using the structure of the causal network and one is using the structure of branchial space actually that's a really interesting way to think about the er equals epr story it's basically to say that the there exists the presence of non-local kind of non-non-standard spatial connections how is that related to the presence of non-local non-standard branch oil connections and is that the case okay that's actually a really good formulation so let me think about that for a second is it the case that inevitably in um in the multi-way causal graph that those two things are related i bet it is i bet it is i bet that the hmm i i'm sure that you know that's something we could probably prove okay thank you to martian there this is this is what i like about um about live stream stuff okay and my my mistake for having taken that at the wrong level um okay christian is asking since brains are part of the universe shouldn't artificial intelligence be possible to model using the same structures yes but remember it's happening at a very different level yes i mean absolutely artificial intelligence is a story of computation everything we're dealing with is a story of computation whether the things i mean the the big deal of artificial intelligence is not that we get computation that's easy to get the big deal of artificial intelligence is can we get computation that aligns with the human things that we care about with deciding that's a picture of a cat or a dog those kinds of things um and that's the the question of of that's really a question of is the universe expected to be comprehensible that is ai okay this is an interesting circular question so the this the statement ai connects to computation is ai is the human understandable analog you know piece of computation in a sense the universe just does its thing and the question is is the universe expected to be connected to something human understandable is it expected to be an ai-like computation or merely a random computation out there in the universe of all possible computations okay so here's where it gets circular we exist in the universe we succeed in operating in the universe maybe our way of being constructed is one which has the feature that that inevitably the universe seems comprehensible to us otherwise we wouldn't be able to operate in other words the fact that there is coherence to physical laws is a consequence not so much of how the universe operates but how we how we are constructed that there are there are versions of us that could not conclude that there are coherent physical laws but we wouldn't have a very interesting time in the universe and so the very fact that we sort of exist in the universe and can have all the discussions that we're having is a consequence that we happen to be things that exist in the universe in a way for which the universe is comprehensible so in that sense maybe there is a connection between sort of the the ai as a comprehensible computation and the universe has a comprehensible computation comprehensible to us because we are things constructed to be to make the universe comprehensible so to speak so that's a possible um a possible connection there um and we have to go real soon here but but uh saint asks what do we think of roger penrose's idea of cyclic universes um i don't really have anything particularly to say about that i mean i think that roger has various ideas about entropy in the universe which i'm not sure i don't know quite a lot of you know when we talk about twister spaces that's a roger penrose production twister spaces are a whole roger penrose production um the uh a lot of kind of for roger penrose's thought for many many years about about sort of sweetness and space time with rather different foundations from the ones that we're using but i suspect that what he has is can be thought of as some kind of effective model in some limit of what we're talking about cyclic universe idea i think is very much driven by ideas about about entropy and gravitational entropy and and those kinds of things which i i don't know how they relate to what we're dealing with jonathan you want to comment on that yeah okay so i mean let me just quickly give a give us some my summary of how of roger's um what's called ccc conformal cyclic cosmology um which i my conjecture is it'll ultimately be related to some uh infinite future versus infinite past limit of the causal network actually being the same um and so um basically so how cc works is you say okay in in the infinite future of cosmology where you know all everything's coalesced into black holes and then all black holes have evaporated so in fact you just have photons left then you know you only have null rays in your space time and uh null rays don't have any notion of time right they they they lie only on the on the on the boundaries of light cones and so there's so in such a universe in the infinite future there's no way of consistently defining a time function and if there's no way of consistently defining a time function there's no way of consistently defining a distance either so in effect or you lose all information about space-time volumes which means you lose one-tenth of the metric information so the remaining nine-tenths of the metric are associated with the causal structure which is the conformally invariant structure of space-time that that still remains that's the thing that's determined by the light rays so roger's idea was that's very similar to what happens in the very early universe where where energies are so high that again you basically lose one tenth of the metric and you only care about causal structure and so his argument is well given that in the these two limits are the same you can do a conformal rescaling of the infinite future and you get something that looks identical to the infinite past um and so because our because the causal graphs that we're plotting are exactly a plot of the conformal structure of space-time uh the you know penrose's idea would basically be some statement about how uh there's an effective theory of the infinite time future of the causal network which makes it look like the you know the infinite past theory of the causal network i think you know i i hate to admit it but i last heard roger penrose talk about this theory in either 1975 or 1976 and the description that you've given of it is definitely more advanced than the description he gave at that time so good for him um but i'm a little embarrassed because i realize i am i am a solid you know 45 years out of date or something on this theory um okay because at that time it was all talked about in terms of the you know conformal flatness of the vile tense and um arguments about gravitational entropy and so on okay that's a much cleaner version yeah there's a way of formulating it in terms of vial curvature and things but that you but yeah he cleaned it up he cleaned it up a lot from from okay but any case but this idea that in the future it's all photons and they have no notion of time that's a very bizarre idea i mean that that's a i mean the claim would be that in the future wow that's a bizarre idea why does he think that the photons aren't going to condense again into something else why do you think that the photon photon interactions won't eventually lead to you know proton antiproton pairs which will eventually get separated which will eventually lead to stars and things again well i assume if you have infinite expansion eventually you know every photon is contained in its own little cosmological horizon if you have infinite expansion but that assumes that you know rapid acceleration of the expansion right which you don't have in a photon dominated universe it just does its thing it's like of you know it's like frw but but just with a radiation-dominated universe right which is nothing special right right so i i i yeah i agree i i don't i don't really know i i'm not even every time i've heard roger speak about it or i i've seen him write about it he always sort of broaches the idea with a certain amount of embarrassment which makes me think that he i'm not even sure that he necessarily believes it's true i think he's he's postulated it's like the claim that there's a heat death to the universe which i now don't believe because the heat death to the universe is just saying the features of the universe that we think about uh are not being just that don't seem to be interesting but there are other features the microscopic details of where all those photons are going and so on that has a lot of information in it it's just one information that right now we are saying forget it we don't care about that um i mean i think that the um uh yeah that's that's but that's your statement about the um uh you know the fact that at the beginning of the universe the causal graph of the beginning of the universe and the what you're saying is nothing much happens late in the universe but also we perceive our perception apparatus also is running very slowly and therefore the um um uh uh the the um the the the kind of um and so we don't notice in the beginning of the universe a lot happened in the first 10 to the minus 10 seconds of the universe but the causal graph has lots of stuff going on and if we were brains in that first 10 minus 10 seconds we would perceive lots to have happened but 10 to the 100 years after the beginning of the universe it's all just photons but we're just photons too and so we don't perceive it doesn't we we are as much perceiving that things are happening as we ever did i mean this somewhat reminds me of of my my longtime friend john mazuris who who happened to be a graduate student of uh got his phd with roger penrose long ago although mostly he's been in the semiconductor industry since but but um he had this he has this bizarre theory of of uh i think the the funny version of it is the creatures of light theory um that basically you know intelligence says you can have intelligences and operating photons i i hadn't really realized i'm not sure he's thought about this infinite future version of uh eventually the universe is all just photons and then the question is you know can you can you sort of operate um you know can you operate an intelligence just in photons the answer is obviously yes i mean this is a feature of computational equivalence that is sort of the answer is obviously yes and then the question is in that future i had not thought about that that's a very interesting case of my kind of physics of alien intelligences is is what does the universe look like if your brain is made of photons good question another thing to pin to our a list of things to think about okay that's a where where yeah everything is conformal and variant um let's see uh a question from loke do you think the space wall possible touring machines that produce some universe could be reduced to some finite set of turing machines well that's sort of the story of universal computation in fact back 12 years ago we found this the very simplest possible universal turing machine and that one universal turing machine tiny little thing um is can be programmed to do what any other turing machine can do so in that sense yes you can sort of pull everything back to that one case a question from n a here opinion on dna computing let's not do that here we can do that another time um the the uh that's a story of i mean more more relevant to us is quantum computing which is more directly related to our models and which we do have a bunch of stuff to say about the question from bob here has the model predicted the dirac equation yet no but we really need to do that that's a story of of of spinners and fermions and so on and we we really should be able to do that i i think we should be able to get the dirac equation but we haven't got it yet um admiral is asking uh close time like curves okay so this is a reference to some paper that we i certainly know nothing about logic of quantum mechanics derived from classical general relativity i i don't know about this i mean that's a jonathan jonathan and other folks uh uh look at these kinds of papers all the time i'm i'm um i hadn't actually seen this one before uh and having only read the i i don't know anything about it i've only read the abstract um but it does seem somewhat relevant because um what it seems to be doing uh is so it okay it's it's known that uh boolean algebras form the you know can be made to form these structures called orthomodular lattices and so and and quantum logics uh can basically if you if you weaken some distributivity conditions over the over the boolean algebras you get uh sort of quantum logics and uh and we actually make some use of that in the analysis that i did at least of multi-way evolution graphs uh one way you can re you can reconstruct aspects of quantum mechanics is by treating the multi-evolution graph as being an orthomodular lattice which you can do as long as it satisfies certain strong causal and variance conditions and what it seem what this paper seems to be talking about is kind of formulating a theory of relativity over these orthomodular lattices or possibly the other way around um i was just disappointed flipping through it i thought it was going to get into a big complicated development but it's actually very short and it just ended which is as it just looked like it was getting interesting here but yes it seems to be it seems to be a description of kind of a a a coarse-grained logic of of of general relativity right right which is basically what we're trying to do you know with this study of multi-way causal graphs um well good good paper to put on our collection of um of possibly related things what we're trying to have on on the website we have a we're sort of collecting all possible uh things that we think might be seriously related um and uh um uh yeah this is um uh right so we have a final a final comment here from richard saying in this panerai's picture the photons may decay and you'd end up with the universe consisting only of neutrinos and anti-instruments that i think is old news because it used to be thought that neutrinos were massless nowadays we kind of think that neutrinos do have some small mass so in in that boy i don't know i mean the the long future of the universe what is the universe going to be made of in the end very good question why do we think i mean you know is it you know there are processes there's something called the erka process which goes is gamma photon photon goes neutrino antineutrino it's a process that might happen in in some stars um and it's a um uh it's a in quantum in well in in uh standard model it would be a box diagram fileman diagram with a virtual box in it um but uh it would be um um yeah is the future of the universe when everything has decayed is it all photons does it have neutrinos what happens i mean i think there's one of these things where the limit of the limit of limit um uh i i don't know i haven't thought about this it's the um what is it called eschatology is that the right pronunciation i don't remember that what's the right pronunciation of the the the end of things the study of the end of things yeah eschatology eschatology okay um right the uh um inaudible what's that there's in philosophy there's some distinction between inaugurated and particularly in theology there's a distinction between inaugurated and uninaugurated eschatology does that mean which is about where whether you basically whether you find out only about what happens at the end when you die or whether it's possible to find out sooner is the fundamental distinction so there's you know there's a school of thought that just says you know wait and see and that's that's how you find out what happens and then there's the there's the inaugurated i think it's the inaugurated especially the people who think that it's possible to know to figure out what's going to happen at the end even you know the sad thing about all of this is that in a sense you know brains operate and we think about stuff and then brains stop operating and that stopping operating of you know is is very much like space like singularities it's very much like it's an end of time type thing and it's kind of interesting to notice that you know when we think about i mean in a different situation you know when you're falling into a black hole different scenario then you get to see the whole future of the universe happen in um uh and so in a sense that that would be your that your i don't know whether it's an inaugurated uh you know eschatology is you know you're falling into a black hole it's kind of you're kind of toast but at least you get to see the whole future of the universe and you get to answer these questions like you know does it end with with a bunch of photons and so on presumably um anyway all right i think it's time to with that um it's it's time to wrap up here uh and it's a comment actually from richard about algebras of graft rewriting by nicholas bear we don't know about this it seems like that's something you should go look up i i think we did add this to our external references i believe okay um we we definitely got some stuff by bear he's yeah he's done some relevant things okay well listen we should wrap up here thanks for joining us um and uh look forward to chatting about more things in future and we are we are rushing to try and actually write down some of the things that we were talking about here um so that they'll be more coherent and and more readable and um look forward to another time all right see you later

Channel: Wolfram

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Keywords: Wolfram, Physics, Wolfram Physics, Wolfram Physics Project, Stephen Wolfram, Science, Technology, Wolfram Language, Mathematica, Programming, Engineering, Math, Mathematics, Nature, A New Kind of Science, NKS, Computer Science, Philosophy

Id: OKGeU6wfSSA

Length: 173min 28sec (10408 seconds)

Published: Tue Oct 13 2020