Wolfram Physics Project Launch

okay hello everyone well thanks for joining me here today we are going to be talking about getting to the fundamental theory physics now I never expected this if you'd asked me even last fall I would have said that I have an idea but I don't know if it's going to work and I'm really excited to say that it's working and I think we now have a real path to the fundamental theory physics I think we've come a long way we're not actually at the end we're not there yet and I'm sort of hoping that all of us together can really finish this job so I want to tell you kind of here where we're at so far I mean it's been a long road for me I first got interested in physics nearly 50 years ago now and I started doing physics when I was a kid I used to do physics for a living but as many of you may know I've spent most of my life sort of pursuing the idea of computation which is a really powerful idea and it's actually what's leading us to the physics we'll be talking about here today and I've sort of spent my life alternating between doing science and doing technology with the idea of computation and one of the things that happened as a result of that is that back in the 1980s I started studying this kind of universe of simple programs and I discovered this amazing thing that even when the programs that you're looking at are very simple even when the rules you set up a very simple the behavior you can get can be incredibly complicated and that kind of discovery sort of put me on a path that led to all kinds of things and it got me wondering about whether maybe that's how physics works maybe there's some very simple rule underneath everything that exists in our universe that leads to everything we see and I kind of had a definite idea about how this might work back in the 1990's um and I started working on it and I actually wrote about a hundred pages about that idea and its consequences in this well they're here this big book that I wrote him back in 2002 um but um and actually in the end as I now realize I got really close to figuring out what we've now figured out but he didn't figure it out back then and I ended up hibernating this idea for a long time doing things like both mouth for an open language and so on and I always wanted to get back to this and I was always kind of thinking about it um and then a little over a year ago I had kind of a little idea that got me a little bit more infused and then two young physicists Jonathan gorod and Max piss Knopf who came to our annual summer school got really excited about this and said you have to work on this and we're going to help you do it and that's what really got me started again and we started really working on this last fall and it was a totally amazing experience because as I say I've been interested in physics for 50 years and there are all these things about physics that I've known about about quantum mechanics about relativity all these kinds of things and suddenly it all started falling into place it all started making sense we started realizing how the stuff really works and it was just great and I want to try and tell you a little bit about that experience here today really the thing that I think is most spectacular about it is how beautiful the whole thing is how how all these different pieces fit together in this really beautiful way and I should say that what we've done would not in any way be possible without sort of all of the achievements of physics so far I mean basically what we're doing leverages particularly the two great developments of 20th century physics general relativity and quantum field theory without those we wouldn't be able to get to where we are and so and the other thing I want to say is that um one of the things that's been really neat is that there been lots of modern developments in physics and mathematics and it turns out that an awful lot of those seem to fit beautifully together with the things that we figured out about physics and so it isn't one of these cases where it's like something new is coming in you throw out all the old stuff it's no we have a kind of a new foundation but all this other stuff that's been being worked on it fits in beautifully and I think it's going to be something very very wonderful to see well so I want to tell you all about this here today and hopefully get your help in finishing this job of course the timing of this is totally weird because we're right now in the middle of this terrible pandemic I mean our company has been off curating data and doing modeling and helping where we can with pandemic kinds of things but I figured that among other things while we're all stuck at home people might enjoy some physics and this kind of a strange historical resonance with all of us because back in 1665 there was also a plague and a chap called Isaac Newton had to leave Cambridge University and go hang out at home and while he was doing that he kind of figured out the basic ideas of calculus and his theory of gravity well we may not be able to match old Isaac but while we're stuck in this pandemic maybe we can all figure out physics alright so let me show you what we have so far so what I'm gonna do here is I'm gonna go through sort of a basic outline there's there's a lot to say but I'll go through a basic outline then we'll have a QA here today then tomorrow we'll be doing a more technical QA for physicists and mathematicians followed by one talking about more sort of philosophical implications then on Thursday we'll do a QA for computer science folks and then we'll be starting of kind of live streams of actually doing this project we really want to make this as open a project as we can and as part of that we'll be live-streaming our kind of working sessions and and our discussions with other people about this project and we hope lots of people can participate in those all right well let me let me get started really here okay yeah you and start all right so let me start off this is the website and you can find most of stuff I'll be talking about here today summer on this website um there's probably about a thousand pages of material on this website let me let me just point you to a few pieces of this which maybe will be useful first of all there's a an announcement here this is kind of a a basic outline was supposed to be a short announcement it turns out it's about 60 or 70 pages but but it's kind of an outline of what we're doing here oops I'm being told I'm not showing my spoon so let's check that [Music] that is bad hold on boom there we go okay well let's start that again so I was I was saying this is the this is our main website that just went live there's about a thousand pages of material here and I let me go through a few few pieces of this um the here's some um okay the so that there's some our main announcement there's kind of a another piece that I've written which is kind of about the backstory of this project kind of how we got here then there is a kind of technical introduction that I've written it's some kind of describes some in more detail kind of how the models that we're discussing work then there are an area for technical documents and related material that includes a couple of papers by Jonathan that for people who are kind of equations first readers particularly professional physicists I would encourage you to check out some of Jonathan's work here um then there is an area here of software tools one of the things we're doing is to make all the tools for doing the things that we've been doing completely available they're available today and you should be able to run them and Wolfram cloud or anywhere where you're running Wolfram language and that's a way that we hope people can start to bus as beta miss um I'll be talking more about some of these other things later there's a registry of notable universe models we'll be talking about that a bit more late there's also I'd like to point you to the QA we've answered some of the what we think of as the most obvious questions here as questions come in we'll try and answer more of them but I encourage you to check that out also um okay well let's get down to business how do we think physics basically works well here's a here's a kind of a a pictorial outline of of things and this looks kind of complicated I guess that might be because our universe is ultimately kind of complicated but this is a lot simpler than that this is kind of showing way down below underneath our universe so I'm gonna be talking about different parts of this I'm gonna be talking about how we start from this very simple kind of rule how we build up a structure that represents space in our universe how we understand how time works how we derive from the properties of space and time relativity special relativity general activity the theory of gravity I'm going to be talking about how the different paths that you can follow in applying this rule correspond to the different paths that can occur in quantum mechanics and the way in which one gets this sort of entanglement of states in quantum mechanics and how how that emerges in these models and in a sense one of the most spectacular things that happens is that it turns out that relativity and quantum mechanics are in some sense the same idea in these models there's a sort of complete unification of the notions of relativity and quantum mechanics which is one of the most beautiful things I think that comes out of this and sort of in the middle of a bunch of those things are things about black holes and the quantum mechanics of black holes um let's see people are asking for me to zoom in a bit here I think unfortunately if i zoom I will okay there we go I encourage you to just look at this for yourself on the web this is under the visual summary on the website okay well let's sum let's start in on on how this stuff works so the thing that we're interested in is to figure out if there is a rule underneath the universe what might that rule be like and if the rule is going to be at all simple we pretty much know that nothing that we are familiar with in the universe is going to be immediately evident in that rule we're not going to be able to see that the rule has a three for the number of dimensions of space we're not gonna be able to see that the rule has some case for some particular detail of the properties of the electron and so on that rule has to be something that sort of packages everything about the universe into some tiny bundle from which all the things that we we observe must emerge so what I realized long ago is that we need that rule to be as kind of minimal and structureless as possible and we need to have something that sort of allows the possibility of everything that we see in the universe emerging now one of the things that is sort of a basic feature of this rule is we don't get to have any notion of space intrinsically in this rule and so we have to kind of make space out of something and in the end one of the things that's sort of a first surprise is the idea that happens in these models that space is something discrete space is made out of a bunch of discrete points that are kind of going to be knitted together and traditionally for the last couple of thousand years actually people have kind of assumed that space is somehow a continuous thing that you can just say I'm going to pick any position in space it will be specified by some precise triple of numbers for example and that's how we define that we can do that we can pick any possible position in space what happens in these models among among other things is that that's no longer possible and instead we're making space out of these discrete elements and one of the other things about these models I said it's very minimal very kind of very little that gets put in from the beginning in a sense everything is just space and all of the features of that we are familiar with about matter and elementary particles and all these kinds of things ultimately will emerge as features of space okay so let's talk about what the rules for kind of doing things in might might look like okay so what we're going to be talking about are rules which we can represent as rules for hypergraphs or we'll talk about those in a minute but we can think about them as rules for for graphs or networks and so for example we might start off by saying let's imagine that we have a some structure like this and we have these elements we're just numbering them 1 2 3 4 and then we have some rule that says how we're going to update this by just looking at the different patterns of elements here what are we going to do to this to the structure and it's sort of an embarrassing thing to admit but the the basic idea for how these rules work is something that is sort of also the foundation for kind of the symbolic programming that is the foundation for often language and is actually the foundation for pretty much all of the practical things I've done in computation for the last 40 years and the embarrassing thing is that I didn't realize that sort of the essence of that symbolic programming idea was exactly what's needed to understand how to build physics out of and I was working on sort of a slightly different way of setting this up but but that the essence of that idea it turns out of the essence of the idea that looks like we need for physics though is just an example of a essentially a rule this is just a sort of more algebraic representation of the thing I was showing earlier this rule that tells us how to replace one sort of structure in our graph with another structure okay so let's say we start off with some some graph that looks like this then let's just try applying that rule a few times this is what we get so the beginning then we apply the rule apply it again again again again again and eventually we're getting something like this so this is this is kind of the story that I first learned in the 1980s that even when the rule is very simple the behavior and the structure that you get can be complicated so this is an example of what what you get off to just running maybe ten steps or something with that particular underlying rule so you can say so what's in the end going to happen is we're gonna run this rule maybe ten to the four hundred times or a rule like this maybe ten to the four hundred times and that's going to build our universe now I will say at the outset we don't yet know exactly what the right underlying rule is we have it's going to turn out that an awful lot of what shows up in physics and this is one of the big surprises it's quite generic and actually quite independent of the details of this underlying rule so we can already derive lots and lots of physics without knowing this final ultimate underlying rule one of the things we want to find is what that final ultimate underlying rule is but you can but so if we ask ourselves well what what kinds of things happen with different rules here are just a few examples of things that happen with some of the simplest possible rules and what we're anticipating is that when we look at enough of these rules eventually one of them will turn out to be the rule for our particular physical universe I'm going to make a little footnote to that I'll explain later why in a sense there can be many different rules that all represent our universe but we'll we'll get to that in more detail later um in a in a sense the I mean this is the sort of process of looking at all these rules and seeing what happens it's sort of a very zoological thing it's very it's as if you're looking at all these different possible creatures in the computational universe and you're trying to find the one that actually corresponds to our physical universe but so all kinds of different behaviors can occur and this is this is what we're interesting looking at okay so first question is how do you get something like space as we know it so the basic idea is that when you're looking at the kind of large scale limit of one of these structures after it's growing for a very long time you'll have something which to a high degree of approximation seems like the space that we're familiar with so it's kind of an analogy that one's very familiar with that we've known about for maybe 150 years although it wasn't it was guessed even much before that that something like a fluid like water that seems to us continuous it seems to sort of flow continuously we actually know that ultimately it consists of a bunch of discrete molecules bouncing around and I think the same thing is essentially what's happening in space that space is just a bunch of discrete points but on a large scale it seems to us like something continuous that we can apply mathematics like calculus and so on - okay so how can we see that more more precisely let's take a look at a a particular very simple rule there's just one of these one of these specific rules and this is the first few steps of what it does and if you keep going for a while longer you'll discover that it start seeing it here it's kind of knitting this structure keep going for a while longer you'll find that it knits a structure like this keeps going keeps going keeps knitting this structure well when we look at the structure we can kind of make a reasonable guess that in the end this is going to be kind of like ordinary space it's going to be like a plane that's just a mesh that corresponds to a sort of two-dimensional space and that's some so that this particular case is very easy to see how the thing produces something that's kind of like space so but things aren't always that simple here's an example of another another rule this makes a structure like this understanding the limit of this is more complicated here's another one this makes a structure like this which we can again kind of recognize is something that's a little bit like our sort of traditional mathematical object with a two-dimensional surface or something actually if you if you project that into 3d and kind of fill it in it'll make a structure that looks like this okay so what we've got underneath is just this discrete collection of points and all we know is which point is joined to which point we don't know there's nothing that intrinsically tells us that the things should lay out in as as a structure like this all we know is kind of the connectivity information for this for this network I might mention one one point is that the actual underlying thing that we have here is a thing called a hyper graph it's a generalization of a graph where instead of just having points joined by one point joined to one other by a connection you can have a hyper edge in which you have multiple points that are all joined together by a hyper edge that's just sort of a detail of how we're building things but it's why we'll refer to the structure that we think limits to physical space as being the spatial hyper graph okay so let's say we want to analyze what's happening in a system like this how would we do that well one one question would be given that we have a a structure that looks like this and we look at it for with a very large number of points in it what what dimensional space might this correspond to well actually there's a pretty simple way to determine that and his heart works since there's a little bit of mathy stuff but it's not not too bad um so if we think about a two dimensional grid let me just say let's start at a point in the middle of this two dimensional grid and let's keep going two points that are one distance one step away on the grid from the points we've already got to let's keep growing that structure and see what we get well one of the things you'll see here is if we just count how many points we got to after we went let's say our steps we'll discover that the number of points we got two is about R squared so that squared in the R squared that two in the R squared that two is the thing that represents the fact that this is behaving like two-dimensional space it's behaving like just a a grid on a plane if we do the same thing in a 3d in a graph that's made to correspond to a 3d grid we'll find out that that same we do that same computation we'll find out that the number of points we get to is about R cubed so in other words the and that's that cubed is what tells us that um we've got something that is behaving like three dimensional space okay well we can do exactly the same thing in one of these structures here we just start from one point and we keep going two points that are one one more step at each one of these away from the points we got two already and then we can ask the question if we do this how many points do we reach after we've gone our steps okay and we can start plotting that and we can it's a little bit complicated because there's sort of multiple things happening where we're kind of evolving the structure so the structure is getting bigger and we're also asking for these kind of balls of points that we're looking at we're asking what happens as they get bigger but anyway when we do that we'll find out these are just curves that represent the essentially the logarithmic difference of growth well its growth rate represents it sort of fitting that exponent and so what we see here is that exponent is roughly fit by about two point seven or so so what that means is that that structure that we had this thing here in the limit this thing is behaving roughly like two point seven dimensional space it's kind of like a a it's not not quite three dimensional space it's more like the kind of thing you would find with fractals and so on where it is behaving like a fractional dimensional space but it's behaving like a a space with a a definite or be it fractional number of dimensions if we go back to something like this and we do that same test we'll find out that in that case when we measure it this thing indeed behaves like it's two dimensional space and if we do the same thing for something like a fractal we can measure that and we'll find out that it behaves like Oh in that particular case of that particular fractal it's about a one point five eight dimensional space okay so this is kind of giving us an idea how do we work out the the dimension of space well another question would be okay we've got space but our universe isn't just space it's got a lot of stuff in it it's got a lot of particles like electrons and photons and all those kinds of things in it and so one question would be how what are those things like particles so the basic picture is this that there's sort of a a background of activity in space where this thing is is sort of bubbling around and lots of connections are changing here but there are certain pieces of this network that have a certain at least local stability to them and those things are the things that correspond to particles that were familiar with so as an analogy for that we can say imagine this network was just cleaner was just everything could be laid out in the plane but imagine that somewhere in that planar network there was a little piece that wasn't quite planar that might correspond to something like a particle in that network it's a thing that sort of locally stable in the network and can move across the network and sort of keep its identity and that's how we think particles work we haven't actually found particles and specific and the more complicated rules here and that's one of the things that we hope to start working on the next few weeks all right so first thing about space is to know what dimension it is and for our universe right now we want that we we know that that number is roughly three as we'll talk about maybe one of the things that comes out of this theory is that the dimension of space might not be exactly three there might be variations in the dimension of space that might be associated with with phenomena and cosmology it might be that in the early universe that a mention of space wasn't exactly three but may have been much larger than three talk about that a little bit more later okay so one feature of space which was discovered comes out of the general activity invented by Einstein in 1915 is the idea that space is not just flat three-dimensional thing it's something that has curvature as well and in fact we can understand the phenomenon of curvature in in these networks here are examples of networks that grew from simple rules I mean kind of get some sense as these networks are laid out here that there's some kind of curvature to the space that corresponds to these networks well that criterion that I told you for working out dimensions of space you can use a similar criteria for working out curvature and just to mention how that works you know when you you might think the area of a circle is PI R squared but if you draw that circle on a sphere its area isn't exactly PI R squared there's a correction that depends on the fact that it is being drawn on a curved object and that's um we can kind of key into that correction so we can work out actually that when we when we do this thing about saying sort of how big is the ball how many points do we get to when we go a certain distance in our system that that will end up not being something which in this plot looks like it's just sort of flat two-dimensional space instead this thing will have a variation and that variation corresponds to coverture and the will will will see all sorts of features of of that curvature one thing I might mention from a mathematical point of view is that what comes out in these models immediately is that what matters to the sort of growth rate of number of points is a thing called the Ricci scalar curvature which turns out to be exactly something that shows up in general but one of the features of curvature is when a space is curved it means that the shortest distance between points is no longer an ordinary straight line so if you were just on this flat space the shortest distance would just be these straight lines on a sphere these so-called gd6 the shortest distances they kind of bow out like this this is a space of negative curvature where the jd6 get squashed together well we can we can look at exactly these kinds of things in our systems and we can and this this is some and well the thing so it's oh by the way in in Einstein's idea of general relativity gravity is associated with the fact that what that when when things travel like a laser beam for example would travel in what it thinks is a straight line but because space is curved that straight line to it is not really a straight line and that non straightness is what is associated with the effect of gravity and we have exactly the same phenomenon and in fact we can we can go ahead and work out the the effective equations for these for what happens with this jd6 and so on and it turns out that the equations one gets for the limit of what happens with is geodesics in our space that's created just from these underlying rules being applied to create this larger and larger spatial hyper graph it turns out that the equations that govern the behavior of these geodesics are exactly Einstein's equations the what what so to begin with a little bit of more technicality to begin with what we're talking about so far is the vacuum Einstein equations the equations that govern essentially the curvature and structure of space itself ok so we can okay so that's a little bit on how space works one another big thing about our universe is time I was sort of describing this as these spatial hyper graphs they just grow but they grow in time how does that time thing work well one feature of traditional the sort of traditional approach to physics is this idea of space time the idea that somehow space and time are in some sense the same kind of thing and that's an idea that kind of gets a lot of special relativity is very much involved with space and time being sort of the same kind of thing but in these models space and time aren't intrinsically the same kind of thing and space is this extent of the spatial hypergraph and time is the kind of inexorable computational process by which that spatial hypergraph evolves it will turn out as I'll explain that even though space and timing these models are fundamentally very different kinds of things it will nevertheless turn out that the all the phenomena of space-time emerge and one gets all of the standard results of relativity and so on but at an intrinsic level space and time aren't the same kind of thing in these models and if I were to pick sort of one potential wrong turn in the history of physics it was probably about a hundred years ago when people started saying space and time really are the same kind of thing and not considering the possibility that that they should be thought of differently it's something that's come out of sort of our computational paradigm that time is this thing that corresponds to sort of the the process of computation and space is something different okay let's talk about time so when I showed this sequence of different steps in the evolution of this graph I was a little bit cheating because what I really should have shown is every individual little update that gets applied by that underlying rule so this is this is a possible set of such updates showing in purple parts of that that got applied so what I was actually showing with the sort of complete steps after sort of every update that could have been applied to this graph had been applied but this is kind of looking underneath looking at every possible update that might have been applied okay so here sort of the the progress of time is about the applying of these updates but now there's a very important thing which is this picture is not the only picture that I could make about how these updates are applied when we're given the underlying rule there Canon general B many different places in this graph where the update could be applied so how do we how does that work well actually what we can think of is this whole graph of all the possible updates that could be applied so here's the the starting state this is one update goes to hear a different update goes to thing which actually looks similar but the arrows will be different here we keep going we'll get to these these different structured states and if we keep going again we'll get to yet more states okay so um - and maybe it's it's sort of a spoiler here that this sort of branching is going to turn out to be what gives us quantum mechanics but for current purposes what I'm explaining is that the sort of progress of time is down the page here and what we're seeing is that there'll be a progression from one spatial hypergraph to another and that corresponds to the progression of time if we continue this graph longer well this is a version of this graph where we didn't arrange it so that it sort of explicitly goes down the page this is just showing the relationship between these different spatial hyper graphs um so okay well let me to sort of explain how this works okay so it's going to be a little bit we're going to get to what we call causal graphs which are a very important concept and they're a bit easier to explain not in the context of spatial hyper graphs but in the context of just rewriting strings of characters so think of it being as like being in a sort of find/replace text editor you've got a big string of text and you're told anytime you see an egg replace it with BBB anytime you see BB you can replace it with a okay so the question is then what happens if you run your text editor sort of in all possible ways so this is a this is what we call a multi way graph of what happens so we might start with an A that can only get BBB but then BBB could give one possible transformation as it gives a B another transformation it gives B a and they keeps going from there okay and so we end up with this whole whole network of possibilities okay so that's analogous to the network of possibilities I was showing you before for special hyper graphs but it's a little bit easier to see in the case of strings um okay so we can we can look at that a little bit more detail this shows what we can think of as the updating events so this starts with an A and then this is the sort of updating event that says a goes to BBB and there's more updating events so this is showing kind of the network of states and events showing sort of how things can progress through time and effect ok so now I'm going to make this even a little bit more complicated because one of the big questions here is what can happen before what and we can think of these updating events as being like below you can think of them sort of computer science really like functions and they have certain inputs and a particular updating event can only occur if all its inputs already into some sense you have this kind of ordering of what what can occur when based on when its inputs are ready so to speak we can draw that here by adding these causal relationships so they're saying this particular thing depends on having on this having happened because it's needs that in order to get its input and so down here there might be something that needs this to have happened in order to get its input and so on and so all these orange lines represent the causal relationships the what thing needed to get its input ready from something that happened before so to speak ok so we can then let's let's now this let's now get rid of the states and just talk about we can call the causal graph that is the the graph that represents the wrote the causal relationships between events this says an event here this event here could only happen after this event here this event here can only happen after this event here this is a a graph of causal relationships okay and this is going to turn out to be sort of a critical thing in understanding a lot of what goes on let me show you so if I kept going a little bit longer and I didn't lay it out sort of starting from the first event I might get some this might be the causal graph of relationships between different events the the threads of causality that join those events okay now let me explain something a very important idea here which is the idea of what we call causal invariants so one of the questions is we've said there are different all sorts of different updates we could do and there are lots of different orderings in which we can apply those updates but it turns out for many kinds of underlying rules it doesn't matter what order we use so long as we respect this causal graph we we we we can do the updates in any order we want okay let's let's show an example of causal invariants in action essentially what causal invariants this this is for a particular rule that is a rule that takes our string of characters and just two at a time sorts them so it says that ba should get turned into a B that's that's all it's doing and this is showing starting from BBB AAA this is showing all the possible ways that BBB AAA can get rewritten with that particular rule and we see these various events that can occur and so on okay so there are all kinds of different things that can happen we can wind up with B a B a a B we can write up with a be be a be a but in the end we're always going to get the same answer in the end we're always going to get a sorted string doesn't matter what sequence of of states we went through we'll always get to the same answer in the end and that's the essence of causal invariants it's actually a property that has been studied in mathematical logic and other places it sort of really x under many different names sometimes called confluence has has a variety of different names that church-rosser property all sorts of other things there's slight technical differences between all these different things but they're basically the same idea how would you know that this idea exists if you've done algebra you might know that when you are doing something like expanding out some polynomial you can say well I'm going to expand this set of parenthesis terms first and then I'm gonna do this one I'm gonna do it in the other order but in the end it doesn't matter what order you do it in that's because that kind of algebra has this confluence or causal invariance property and some of these rules that we're looking at also have that property so this particular sorting rule has that property okay so so so what well the the big so what is then what that's saying is there are these different possible sort of paths of history but it doesn't really matter in some sense which path of history we choose we're always going to sort of get the same behavior in the end okay so for example for this particular thing we can look at what the causal graph that it makes is its causal graph is actually very simple it just looks like this let's look at how this works in sort of actually operating on the original string so here we have a fairly long string and each of these yellow boxes represents an event that represents a rewrite of ba gets turned into a B so this is a particular choice for how we can do that sequence of rewrites I can show you what the causal graph associated with that particular set of rewrites is there it is but there are lots of different causal graphs that I can use and what we'll notice here is that even though the actual particular updates were done in different orders if you look and you just look at the structure of this causal graph it's always the same so it doesn't matter what the underlying order of updates is you'll always get the same causal graph okay well so here's the first big thing that comes from this we get to derive special relativity and that's special relativity is not usually something that one imagines deriving it's something which in a sense ISM is a consequence of sort of axiomatic features of the way physics is set up constancy of the speed of light independence of inertial frames these kinds of things but in these models we get to actually derive special relativity it might not be true in these models but it is true it is a consequence of causal invariance and of various kinds of limits and intrinsic randomness properties and things of these models that one gets special relativity so let me show you roughly how that works so let's let's look at a simple causal graph here's a simple causal graph that has a bunch of events two joined in these simple ways so let's imagine that we the important thing to say is in special relativity one of the sort of big innovations was being more realistic about what an actual observer of the universe can tell is going on so if we sort of look from outside the universe we might be able to see all sorts of things but as an observer embedded in the universe operating according to the same rules as the universe there limits on what we can tell for example we in in the sort of physical case we can't things can only travel at the speed of light so we can't we can't be aware of things yet that was sort of that happened further away than we have been able to see them based on information from them coming at the speed of light so in so there's a question of sort of how do we model that observer how do we model an observer who is embedded inside the system and I might say that for the systems that we're looking at here one of the things you might ask is the if the observer operates according to the same rules as the system itself what what consequences that have let me give you an example of a consequence that have arrived well the bizarre consequence let's say that we were to set up the universe so only one place in the universe ever gets updated at a particular moment so what's then happening it's kind of like a Turing machine in computer science you have this sort of head that's zipping around the universe updating different parts of the universe you might say I can't possibly be the way at the actual universe works I can plainly see that's not what's happening the problem is if you start thinking about it you realize that you can't see anything until in a sense you've been updated and as this head zips around trying to update different things it's it's kind of the the causal network that it is producing is one that actually looks can look pretty much like this where the you can't tell that that thing over there has or hasn't been updated until you yourself have been updated and so when you sort of put all of that together you realize that you get this sort of one integrated causal graph in which in a sense things to you as an observer can sort of seem to happen at the same time even though to something sort of outside the universe you might imagine seeing this head just zipping around doing different things at different times okay so how do we make sort of a a model of what that observer is like the the thing an observer will will do is to say okay I'm gonna decide what counts as successive moments in time for me and so these this is mathematically foliation of this causal graph and this is saying these are the successive moments of time that I as an observer I'm going to decide to identify as this is my definition of time is going to be the sequence of of slices like this okay well the important thing is let's see I have a better picture than that oh yeah here we go so right so this let's imagine that observer is not just stationary but our observer is moving okay so this is a this is now our moving observer to our moving observer that that moving observer will choose their kind of foliation of space-time in a different way if we then if we say well what what will this be perceived like to an observer will realize that the sort of perception to the observer is of something like this where the observer will say okay I'm just having these sequence of simultaneous things of sort of surfaces of simultaneity what are in physics called space like hyper surfaces that the sequence of space like hyper surfaces and then this and that with when I make that transformation my causal graph will seem to me like this okay so what well the so what is that that transformation of the causal graph happens to be exactly the transformation that occurs in special relativity and in fact we can see kind of so what what's happening here is that even though we might start off from this this just simple rule that's operating according to the in this particular way it produces this causal graph once we have this causal graph when we are entities sort of existing in this universe as part of this causal graph we will end up perceiving the operation of the universe to be exactly the way that special relativity says it has to be so one of the phenomena in special relativity that's his time dilation and time dilation is kind of as you will kind of we can kind of see time dilation here in my other picture probably I don't know that one on that term if you're moving in space if you're kind of exploring space more rapidly time will move more slowly for you and let's let's take a look at how that works in these systems so let's let's say we've got something like this this is so time the events are sort of occurring at a certain rate if we now pick a different reference frame if we are effectively traveling at a certain speed in space this is the sequence of underlying events that will perceive and you'll notice that this sort of it takes longer to get to the final answer here than it did when we were just sort of stationary and choosing to to choose our sequence of time moments of time differently and that phenomenon is in fact exactly time dilation and special relativity and the the reason okay so why does this all work the reason this works is because of causal invariants what it's what caused law invariance implies is that even when we are picking this different reference frame that corresponds to going at a different velocity even when we pick a different reference frame it will still be the case that the causal graph that we get out from from the system will be the same and that's a consequence of Goslin variance and so causal invariance implies but relativity now the real situation is a little bit more complicated than I've showed you the real situation this is a slightly more realistic causal gotthe still not really as as wild as they come but this some this is sort of the the foliation of the of this is this whole thing that's built up from this extent of the spatial hypergraph time is just the sort of computational progression of applying update rules it's still the case that when we look at what we as observers inside that universe perceive what we perceive is the causal graph and when there is causal invariants that has the consequence that what we see will satisfy that the the rules of special relativity in a sense the the causal invariance is what leads to the independence of reference frames that special relativity talks about all right so so that was the first I mean it I think it's a big deal I I knew this some in the 1990s actually that from models like this it was possible to derive special relativity um let me tell you something I didn't know at that time which is what things like energy are so one of these so and it's really surprising to me that it's possible to say this as simply as as it'll be possible to say it so I'll just say what the what the final statement is energy is the flux of causal edges through space like hyper surfaces and so what does that mean it means when we look at this picture I made these slices here these are the so called space like hyper surfaces these these things here these are the causal edges and the statement is the energy if we look at some region of the universe and we ask how much energy is in this is there in this region of the universe the answer will be the amount of energy that's there is the basically the density of these causal edges that slice through these space like hyper surfaces and in fact the so that's the that's that's in this model that seems to be what energy corresponds to so momentum for example corresponds to the flux of causal edges not through space like hyper surfaces these horizontal surfaces but through what are called time like hyper surfaces which are the the sort of orthogonal surfaces here so the momentum corresponds to the the flux of these edges through through time like hyper surfaces well now one of the things that comes out in relativity that sort of an assumption in relativity is that space and time have the same relativistic transformation properties as energy momentum in this model that is derive a ball and that comes about because of this fact that that energy represents these slicing through space like hyper surfaces and slicing through time like hyper surfaces when you work it out you'll discover that term that it implies the same special relativistic transformation properties for energy momentum as for space and time okay so another big thing in the world is mass and you can understand mass rest mass in terms of of this as well rest mass is a little bit more complicated to describe but but it is essentially the it relates to kind of the the the the part of energy that kind of does not correspond to communicating with with different pieces of the special hypergraph it's the it's the part of the energy that sort of has to do with a single part of the spacial hypergraph going going going sort of being being rewritten in place so to speak that corresponds to mass so actually I think I even mentioned in the announcement post and I mentioned in more detail on the technical paper and I think Jonathan mentions in even more detail in his technical paper the that that means from those definitions of energy and mass and so on we can simply derive for example a equals MC squared which again is quite remarkable because that's not something that has been derive a ball in physics before that's something that really comes from the sort of axiomatic assumptions of relativity but in this case it's actually derive a ball from sort of the underlying structure of these models okay so so that's some so I should mention another thing the Einstein's equations for for gravity the way Einstein's equations work they say this kind of a version Oh actually that has a okay it's a version of Einstein's equations that talks about the curvature of space that's what's on the left-hand side equals this thing here the energy momentum tensor that has to do with energy and momentum in space well since we think we know what energy momentum is and we think we know what curvature is we should be able to derive this equation and indeed we can and indeed this this equation follows as a result of causal invariants this equation is an inevitable consequence of causal invariants plus a few other kind of mathematical features of these models in fact to say how it works roughly the the main other assumption is that sort of at a microscopic level the sort of individual rewrites that are happening occur in a kind of random way now they're not really random at all they're completely determined but when we look at one of these things it looks to us random it's the same thing that happens I don't know in the digits of pi for example the digits of pi have a completely determined sequence yet when we look at those digits they seem for all practical purposes random and if we do statistics on those digits they'll come up as being just like a random sequence to all of our statistical tests well the same thing happens for the points in space at a very small scale the points in space are completely determined where how they all work and how they're all connected but they seem for all practical purposes random and that effect of randomness allows us to use various kinds of statistical arguments that allow us to derive sort of the continuity of space and so on and essentially we need that kind of intrinsic randomness generation we need one other we need causal variants and we need one other crucial fact and the other crucial fact is that the universe is finite dimensional the universe is not zero dimensional and it's not infinite dimensional and if we put those facts in then we can derive Einstein's equations and it it's actually analogous the derivation is actually surprisingly analogous to the derivation of the equations for fluid flow from knowing about microscopic dynamics of individual molecules and for sort of the same reasons it doesn't matter what the individual molecules look like you still get the same fluid equations it doesn't matter the precise details of the underlying rule here you still get Einstein's equations so kind of another big deal I mean I kind of knew this well I I knew at least the left-hand side of this back in the 1990s that that was de Rivel for models like this but since I didn't know how energy-momentum worked I couldn't really get the right hand-side properly okay so that's that so let me talk a little bit about the other things in the universe so to speak and then I'm going to talk about quantum mechanics after that so let's talk a little bit more about the universe so one question is when when we look at the well okay so let's yeah okay so when we look at the spatial hypergraph and its evolution can do all kinds of things here's one of the bizarre things that can happen a piece of the spatial hypergraph can break off it's like we've got the universe it's all going along just fine and then a piece just breaks off once it's broken off it can never communicate again it's stuck it's some it's a it's a disconnected piece of space-time okay well what does that remind us of that reminds us of black holes and indeed in these models it's pretty natural to form black holes this is a causal graph and this causal graph says you start here and everybody is communicating everybody's going back and forth but then well then it splits and this part of the causal graph splits off from this part of the causal graph this is the inside of a black hole this is sort of the outside of a black hole so that becomes a natural thing that happens in these models the formulation for the formation of singularities and a lot of the phenomena essentially if you are familiar with general activity these causal graphs of ours are very much like the causal diagrams of generality that they are now derive above from something much lower level if we look at um you know what might our universe be like these are just sort of three examples of different kinds of rules this is one that forms a lot of disconnected pieces that these pieces are not space-time disconnected but they are causally disconnected so they will act like black holes this one is a is a weird universe where things don't communicate much with each other this is more like sort of a there's way too simple to be our actual universe but this is more like ordinary space so now one question would be in the very early universe what might it have looked like and one of the things that comes out of this these models is the idea that the very early universe could have been much higher dimensional than our current universe and that turns out to to solve a bunch of problems about inflation and cosmology and so on the idea that you have a universe that starts very high dimensional so that everything can easily communicate and then it only gradually becomes more like three-dimensional now by the way when I keep on talking about dimensions changing and so on there isn't a lot of good math around how to do that typical studies of the way the way things work are based on spaces of fixed dimension and typically integer dimension um and so for example essentially all of calculus is built on the idea that one's looking at sort of continuous spaces of integer dimension and so in order to really one of the things that we need is to figure out essentially a generalization of calculus that works for these fractional dimensional spaces and that also works for spaces which can change their dimension and which can work for things bizarre things like it could be the case that it's possible to reformulate general Authority not in terms of curvature of space but in terms of of dimension change in space so those are some of the some of the kinds of strange things that can happen let me mention one other thing while I'm talking about about structure of space and let's talk a little bit about particles again so you know I've studied cellular automata a lot this is an example of a cellular automaton a cellular automata and unlike the models were using for the for physics now where there's just a bunch of points that are all connected in arbitrary ways a cellular automaton has a very rigid grid it's just a rigid grid of cells each cell is for example either black or white and there's a rule that updates the color of each cell based on its neighbors so it has a very rigid notion of space and time it doesn't have dynamic an emergent space in time it's just you put it in from the beginning and then you see what happens but it's easier to see to actually run simulations and so on there's a particular cellular automata rule 110 and one of the features of this cellular automaton is you can see that it has these kind of like persistent localized structures that develop in the cellular automaton and these behave very much like particles they interact they they they have various rules for colliding etc etc etc this is kind of our this is a kind of an analog of of the particles that we might see in these networks and as I mentioned before we don't yet know in detail how that works there's a I I've been interested in these things for for a long time and I've I've asked for example some of the world's leading graph theorists about how we can understand things about how localized structures might work in graphs and I think a good example of a quote was come back in a hundred years and we may know more about how that works well my hope is that one of the things that we're able to do now is because we can actually simulate this these these things and we actually have we can build up our intuition from actually doing things with computers we might be able to accelerate that hundred years a great deal and that's but um so one thing I might mention about particles is some one thing we would hope is that eventually we can derive from from these underlying rules what particles should exist in the universe and the fact that their electrons and muons and poor leptons and gluons and photons and all those kinds of things let's talk a little bit about that though one of the issues is just because you know the underlying rule doesn't mean that you immediately know its consequences there's a phenomenon I call computational irreducibility that I started studying a lot in the 1980s that basically says that the the process of knowing what will happen even in a system like this can be irreducibly can be something that requires an irreducible amount of computation you might say gosh I don't need to the rule is so simple I can just jump ahead and say this is what's gonna happen and a million steps in the future well it turns out you can prove that you can't do that essentially the reason is that whatever it is that you're going to use to jump ahead is itself like a computer and this thing behaves like a computer and those two things are essentially computers of equal power there's the thing I call the principle of computational equivalence that says that and that we have increasing evidence for and that means that we just don't get to jump ahead it's an irreducible process to know what will happen and that's one of the things when we if we have this underlying rule for the universe to know its consequences requires sort of an irreducible amount of computation and among other things to for example know its consequences for the you know whatever it is the the 14 billion years that our universe has existed we would have to essentially run the computation that corresponds to all those steps of evolution of our universe which we don't get to do in the universe and we don't get to really accelerate it much because of computational irreducibility now the good news about computational irreducibility is that whenever there's computational irreducibility there are always pockets of reduced ability they're always pockets of places where you can jump ahead and those are the pockets that we have to kind of live in when we try and actually understand the how the physics of our universe emerges from these underlying rules actually I should say one of the one of the sort of spectacular things that I really do not expect at all is that in these models that involve these hyper graphs and and so on it turns out that there's kind of a layer of reducibility that sits on top of this sort of underlying computational irreducible let's say and that layer of reducibility is precisely what allows us to derive things like general relativity and will allow us to derive quantum mechanics it's the fact that in these models for reasons I did not expect although it's sort of obvious after the fact there are things about them that are both generic and don't depend on the precise details of the underlying rules and are not kind of ensnared by this by this kind of irreducible difficulty of computational or disability so that's that's an important piece of why it's been possible to do this project so far and we don't know exactly how far this computational reducibility is going to go and we don't know for example whether it will allow us to derive things like features of local gauge invariants I'm kind of expecting that it will and we don't know whether it will go as far as telling us things like particle masses my guess is it won't and that those will be specific to particular rules but anyway so we can start to try and work these things out I might just mention one thing we know certain particles they've been discovered by particle accelerators and all these kinds of things um we've got sort of a mystery in the universe that it seems like a large fraction of the matter in the universe is dark matter that we don't know what it is yet so sort of the hunt has been on for what that might be in our models the there are a bunch of there's a sort of a question of what the spectrum of particles might be like so one feature I'll talk about a little bit more later is it turns out that an electron which is kind of the lightest nonzero mass particle except for kind of the neutrinos which have a weird way of having mass the that we know about but in in our models for reasons I'll try to explain there's reason to think that there might be particles incredibly much lighter than the electron that are like 10 to the 20th times lighter than the electron but not of zero mass nonzero mass but very light compared to the electron and that's sort of interesting because that's a potential candidate for for things like dark matter I've called these things Allah gongs reason I call them that is because it comes from the greek word allah gas it means phew and i call them that because they're things that involve their particles that involve few hyper edges in the spatial hypergraph and so that's one of the things that sort of a a prediction of this model is the expectation we don't know exactly where those particles will be but that there will be particles very light compared to the electron that will exist um the okay so the somebody's asking what they've sort of captured this image this is the rule 110 so an automaton okay let's go on and talk about quantum mechanics um so let me see what do I have here oh okay all right so one thing so quantum mechanics is this sort of strange feature of physics that was discovered originally around 1900 was the first inkling of it and it really sort of came of age in the 1920s and my friend dick Feynman always used to say nobody really understands quantum mechanics and I know I certainly didn't understand quantum mechanics before really recently um and there's still more to figure out about it but one of the one of the features of of these models is quantum mechanics is not an add-on it's not something where you say oh there's physics we understand classical physics we understand that there are certain laws of motion and things like that oh now we have to add on quantum mechanics that's a another you know another physics course which has to get added on so to speak that's not the way this works it is absolutely inevitable in these models that one has to have quantum mechanics and so the reason that comes about is the thing I was talking about earlier that there are these rules and there isn't just one way the rule can be applied there are many ways the rule can be applied and what we think about is apply the rules in all possible ways and in a sense the these all these different possible ways so what a key feature of quantum mechanics is that it isn't the case that one always says a definite thing happens in sort of classical physics one says you know the ball moves in this trajectory and it's definite in quantum mechanics one says the photon can go this way or it can go that way and there can be in two ference between these different ways that it goes and it's all something where one traditionally is just saying there's a certain probability of measuring it to be this or that um so there's this though these many paths of history that get followed and we only we get to sample sort of the the aggregate results of those different parts of history and that's exactly what's kind of happening here now the so sort of this would be kind of the the classical version is you just have those sequence of strings I'm looking at strings rather than hypergraphs here because it's a bit easier to do that okay so how does how does quantum mechanics then work well these these different possible things correspond to the the again I I well these correspond of the states that one talks about in quantum mechanics eigenstates pure states whatever that one talks about in quantum mechanics ok so here's his sort of a big story of quantum mechanics turns out in quantum mechanics one should think about and thinks about this is the sort of multi way system with all the possible things that can happen in quantum mechanics now imagine that we're an observer also embedded in this multi way system observing it and we are trying to make sense of what's going on in all these different paths that are going on in the different paths going on inside us and so on we're trying to make sense of all of this what we'll end up doing is doing something very much like what we did in space-time we'll make these kind of foliation x' will say where we are going to view our view the world according to this particular in this particular reference frame we call these they were calling these things now quantum observation frames there's kind of a new idea about how to think about quantum mechanics this idea of thinking about it in terms of sort of reference frames a bit like relativity um so one of the things that happens in quantum mechanics is this idea that you make a measurement in quantum mechanics there are all these different possible things that are happening but at some point you say I'm gonna figure out did the electron go that way or this way you make a measurement and then after you've made the measurement it's definite it's never going to change that will be the result of that measurement now one of the things that's been very mysterious in quantum mechanics is the fact that when you that given that there are all these different parts of what can happen how can it be the case that different observers different measurements sort of a consistent how can there be sort of an objective reality in quantum mechanics even as what's coming out is just saying there all these different paths and all these probabilities four paths and so on and so this this model of ours kind of explains that and it turns out that the origin of kind of the objectivity in quantum mechanics the the fact that there is a definite reality in quantum mechanics is precisely the same phenomena of causal invariants even though there are different ways that one can make measurements even though there are different kind of quantum observation frames that one can use one still ends up with a one still ends up with a consistent sort of view of reality and that's a consequence just like in relativity the fact that we got sort of the same laws of physics independent of whether we were moving at different speeds and that corresponds to different reference frames in relativity so here these different quantum observation frames correspond to different sort of slices of viewing reality but nevertheless because of course on variance they all ultimately correspond to the same reality so what I'm showing here is kind of a a cartoon version of a quantum measurement what happens here is the one says when saying okay the quantum system is evolving and then what happens here is the observer is deciding to make a foliation in which they're essentially freezing time they're saying I think this is the way things came out and I'm sticking to that and so I'm basically making these successive time steps all be scrunched together here now again a little bit complicated what's going on here I will make an analogy this is kind of what happens so that this is analogous to what happens in a coordinate singularity in in in general relativity in space-time it's actually analogous to what happens at the the event horizon of a black hole effectively what's happening is that you're freezing time now in this case you're just freezing time by a convention The Observer is choosing this way of setting up time they're choosing to decide that time isn't going to change for them after after they get to this state and turns out when they do that things in order to maintain consistency they they're sort of the region that that is then frozen for them will get larger and larger and that corresponds to quantum decoherence and to sort of the entanglement of states in quantum mechanics ok so this is a super simple case this is a slightly more complicated case the real case is vastly vastly more complicated than this but this gives some idea of how you can have kind of time freezing foliation and this well it turns out when people do quantum computing they really want to freeze the state of a particular qubit they want it to stay as a pure state they say this is the state I want it to stay this way and essentially what they are doing is to form a a black hole in this multi-way space so the thing to understand and sort of a very beautiful analogy I think is that we talked about space-time we talked about how there's a causal graph in space-time we now are talking about the multi-way graph and this is this is there is and we're talking about foliation z-- of the multi-way graph and those foliation czar as I was mentioning directly analogous to the foliation z-- that we do in space-time and so one question that you can ask is ok we are if in when we looked back at um at something like this this was a foliation of a of a causal graph the slices here when we look at these slices and we say what are the states associated with these slices these slices correspond to instantaneous spatial States so they correspond to spatial hypergraphs at a particular moment in time they are the that's what the foliation of the causal graph and space-time corresponds to is spatial hypergraph okay what is the foliation of a multi-way system what does that correspond to okay well we can think of that it turns out as a thing we're calling branch fields space I'm sorry my British accent probably ruins that word but branch she'll um branch she'll um the unfortunate Jonathan also has a British accent and we're the ones who've been talking about this a lot and so we don't really know if this works in American but that's that's the word we're using okay so in this so the slices here correspond to what we call branch field space if we we kind of take that slice and look to the side we'll discover that these successive steps correspond to that the way that that multi-way graph worked they define connections between different states in branch chill space and those connections correspond that are a map essentially of quantum entanglements this is essentially a map of entanglements in quantum in the space of quantum states and so that's a a so this is then we get to kind of analyze sort of in tank the entanglement of quantum states so again there's space-time with this notion of extent in space in the multi way graph the the different nodes in the multi way graph correspond to different quantum states and there is a notion of a space of different quantum states and there is this way that we can kind of knit together these different states by using not sort of positions in space but instead entanglements in branch field space and so that's so then what we've got is this notion of branchial space corresponding to the analog of of physical space but in the space of quantum states okay so that's that's so now we can start asking questions so we've got a whole set up it's a bit like generality we've got because we got some we've got so a bit like relativity we've got these some these foliation x' and and I would say that that when we foliate the space the thing that that what's going down the page here is still time just like it was for space-time but what's going across the page is not physical space it's branching space the space of quantum states and so then we can ask ourselves well is there an analog of general relativity in branch real space and it turns out that there is and essentially what's happening is when we look at gd6 the shortest paths in branch real space those we can we can ask a question like if we want to get from this quantum state to this other quantum state what's the geodesic that goes from one quantum state to another quantum state and we can ask about how those geodesics are affected by the presence of other quantum states and so effectively what ends up happening is that the gd6 in branch real space have went when you want to get from one place in branch chill space one quantum state which is a sort of position of branch of space to another one you're you're going along this gd6 and the geodesics are deformed by the presence of other quantum states and that defamation well the presence of other quantum states okay I have to mention one other thing I mentioned that in space-time energy corresponds to the flux of causal edges through space like hyper surfaces well we can make and it's a slightly more complicated thing just like we can make a causal graph in space-time we can also make a causal graph in multi waste in in branch alone in in the multi way graph and this is a thing called the multi way causal graph and causal invariance implies that the multi way causal graph is essentially can be decomposed into a collection of identical causal graphs corresponding to each different path than the multi way system but basically the this multi way causal graph is a representation of causal relationships not only across through space it's also through branching space it's a representation of the causal relationships that between events that occur both different places in space and at different places in the space of quantum states okay and now it turns out that we can use the exact same definition of energy for the multi way causal graph as we could for the ordinary causal graph its are still a flux of causal edges now in the details of the way that physics works it's always been a bit mysterious how the energy of classical mechanics and particular statistical mechanics relates to the energy that appears in quantum mechanics in this set up the way it works is that they're both fluxes of causal edges they're both fluxes of course alleges that in sense decompose the same way but one of them can be thought of as part of it as flux of edges and the multi way causal graph the other and the ordinary causal graph okay slightly complicated but but that that means that when we are asking about jd6 and Branchville space what we just like in physical space the gd6 the shortest paths are affected by the presence of energy the same thing happens in branch hill space so in other words the the gd6 that determines the the sort of the path that lets you get from one quantum state to another is affected by the presence of essentially energy in the in well in in the system in the represented by a feature of the multi way causal graph okay so what well the big so what is that the analog Weinstein's equations effectively which tells you about the deformation of this gd6 tells you that the presence of energy deforms that makes the gd6 turn and okay in slightly fancier physics when you are talking about energy and momentum there is a relativistically invariant quantity called the Lagrangian which is sort of a combination of those things and turns out what actually matters here is the Lagrangian density and that's what actually turns the gd6 in Branchville space okay well the turning of gd6 in branch real space gives you the equations of motion of quantum mechanics and so that and the most direct way to think about that my friend dick Fineman one of his great achievements was this thing called the path under pole in quantum mechanics which is the mathematical formalism that sort of the the the underpinning of most modern ways to approach quantum mechanics the path integral says you are looking at between one quantum state and another the sort of the world can take many paths but each path is weighted by a particular quantity e to the is over h-bar um and in in this set up we get exactly the path integral in other words when you look at these geodesics on the defamation of these geo d-6 those the way these geodesics are deformed is precisely the way they turn exactly corresponds to this e to the I s thing the we're thinking about and was turning in Branch Hill space you can equivalently think about them in terms of complex numbers but we're effectively thinking about them as vectors in branch real space branch field spaces are white so that's that's a pretty big deal that I think that it's possible to derive the path integral from this underlying structure of a multi-way graph and the multi way causal graph and so on it's also just super cool that the the fundamental fact of quantum mechanics is the same as the fundamental fact of space-time and that essentially the analog of the Einstein equations is the path integral and so we might ask what is branch real space actually like branch real space is very complicated it's a whereas physical space is nice and tame and seems to be roughly three dimensional branch real space is much more complicated and sort of probably exponential dimensional it's kind of like some kind of projective Hilbert space or something it's a complicated thing and we need to understand more about it but we can already say things like these aggregate facts about gd6 and about the path integral without knowing more details about branch field space but to really understand branch field space we have to go and and do more there I should mention that the analogy between quantum mechanics and general relativity has another as another interesting piece so for instance some you might know the uncertainty principle in quantum mechanics that if you if you make a for example if you make a position measurement and then you make a momentum measurement that the one measurement affects the other or effectively that if you and that that corresponds to the formalism of quantum mechanics the non commuting of the operators that represent the operation of doing the position measurement are doing momentum measurement so essentially the what one's saying is you do position than you do momentum and that isn't the same as doing momentum and then position okay so turns out mathematically that is a statement that these operators do not commute okay well in general relativity we have an analogous thing we have so called covariant derivatives we have taking paths in space so you can say let's start let's go horizontally let's go vertically let's go horizontally let's go vertically and when you're in a curved space you know get back to where you started from again and that's that's a consequence of curvature it's represented by the Riemann tensor in in in standard differential geometry and in studies of space-time well it turns out that that exact same phenomenon happens in branch real space you have the same you don't get back to where you started from in branch real space when you apply these two operators in two different orders and that's exactly the uncertainty principle um then there are all kinds of other things that you can derive in quantum mechanics and Jonathan has written a nice paper that goes through some of the mathematical details of that um but anyway that that's the okay so let me let me now mention a couple of things here um and I'm getting closer to the end here I'm going to talk a little bit about some of this sort of what what this all means and so on but but let's talk about this sort of analogy between space-time and Branch Hill space the space of quantum states this is a very very simplified representation of a multi-way causal graph in which we're essentially seeing kind of edges that correspond to the edges that correspond to this is sort of the time direction and we're seeing there's extent in space and there's extent in branch Hill space okay so this is we're now seeing sort of together sort of physical space and branching space most of the time physical space and branch field space don't really get together much near black holes they can get together and all sorts of fun things happen but let me mention another feature of this so in space-time one thing that happens is there's a maximum speed at which information can propagate and that's the speed of light and we can see that in these some in these models because in a causal graph the the maximum rate of information propagation here let me pull up a causal graph here the information propagates by going from one event to another and we can make up light cones effectively by saying which events are in the future light cone which events can be got to from this event here and that the you can only get to a certain cone of events in the future of that event and the width of that cone essentially corresponds to the speed of light and in a sense the conversion from a an elementary time going down here to an elementary distance in space going across that conversion factor is precisely the speed of light okay so in branch real space the same kind of thing happens in the multi way causal graph you can make also cones that aren't light cones there now what we call entanglement cones they're cones that represent the maximum speed at which you can entangle new quantum states so they represent sort of a limit to to the rate of kind of measuring more quantum degrees of freedom just as the in this in the case of basse they represent the the speed of light represents the maximum rate of kind of sampling new parts of space so the maximum entanglement speed represents the maximum rate of sampling new parts of quantum space new quantum states okay so that maximum entanglement speed has some has well all kinds of all kinds of consequences let me mention one thing that relates to black holes in so in a black hole there's an event horizon and the event horizon is associated with the fact that well you can think of it as a black hole is something where the escape velocity of the black hole is more than the speed of light nothing can get out of the out of the event horizon around the black hole that comes up that in our models that event horizon is associated with a separation a disconnection in the causal graph that corresponds to effects that can't can't propagate from one side of the event horizon to the other so in addition to a physical event horizon associated with the the space-time causal graph in our models there's also an entanglement event horizon that's associated one can think of it as also exceeding the entanglement to maximal entanglement speed that effects would have to exceed the maximum entanglement speed and so all sorts of bizarre things happen so there's an entanglement horizon that actually sits outside of the causal event horizon so and the entanglement horizon is not localized in physical space it's localized in bronchial space but it's something that's outside the space-time event horizon and so that if you follow the theory of black holes there's been sort of a information paradox about black holes that has to do with where do the quantum degrees of freedom that sort of reside between a black hole that starts and a black hole that eventually evaporates in Hawking radiation and I think we now kind of understand a way in which that works which actually dovetails very nicely with a bunch of recent thinking about um that's happened in particularly in the 80s CFT correspondence and in the ER equals EPR work that's been done recently in in theory of black holes and so on but in a case the in our in our picture what happens is there's this entanglement arising that sort of sits outside of the causal event horizon and there can be sort of quantum degrees of freedom that exists there and are preserved even when the black hole forms okay let me mention one bizarre thing what happens so in a in a black hole I think in Russian black holes are called frozen stars and the reason for that is that if you look at a black hole from a from a great distance it will never altom utley seem to form so and what will happen is for example if you're looking at a spacecraft that's falling into the black hole falling through the event horizon to you as an outside observer it will seem to be freezing time right at that event horizon it will not it will never seem to go over the event horizon to an to a distant observer and actually that freezing of time Atem at the event horizon is exactly the same kind of thing as is happening here this when you try to make a qubit in a quantum computer what you're effectively doing is to make a black hole in branch hill space to try and freeze time around your qubit to prevent it from being affected by the rest of the universe same thing is but now in in the analysis of black holes so in spatial in physical space they're effectively freezing time as you go over the causal event horizon what happens you go over the entanglement event horizon well if you're an observer there and you something rather bizarre happens effectively you are oh I should mention another thing when you go through the event horizon when you go into a black hole you get what's often technically called spaghettified you get elongated very sort of by the tidal forces of the of gravitation you get kind of extended in space well the same thing happens that the entanglement arise and you get expend extended in branching space and one of the consequences of all of this is you basically can't do a quantum measurement there it becomes infinitely difficult to do a definitive measurement so a way to think about this is at the entanglement horizon an observer can no longer form a classical thought they can no longer come up with a definite conclusion about what happens they will always be stuck sort of having this quantum indeterminacy and that means for example if they ask you know when they have a couple of particles like a pair of particles and you say did did the particle fall into the black hole or not the quantum The Observer stuck at the entanglement horizon will say oh I don't know I can't form the definite classical thought of whether the particle felons a black hole or didn't that's just one of the weird things that happens in the at the entanglement horizon that's one of the places so so let me show you something so one question is I've talked about this structure of of space and how it might be discrete and so on let me so one question you might ask is how big are these some how big are these little little connections in space and I forgot to make a slide here but so I have to show you um actually I might just mention in my more technical paper there's kind of a table of what the different kinds of things that we know about in physics correspond to so things like local gauge invariants the expansion of the universe conservation of energy microscopic reversibility all these kinds of things virtual particles all these kinds of things that one discusses in physics we're trying to understand the analog of those in our models by the way I might mention one big analog is some in terms of cosmology one of the mysteries of cosmology has been that when you try and mix quantum field theory with general activity there's sort of an incompatibility in cosmology because quantum field theory says there's sort of an uncertainty principle about particles that says that in a quantum field you don't know how many particles there really are there and there's sort of this infinite soup of virtual particles that are getting produced and those virtual particles will have an energy density that's absolutely huge and that energy density would roll according to them applied that energy density and Einstein's equations it would roll the universe up into a tiny ball well in our models that doesn't happen and the reason that doesn't happen is because those virtual particles that all of that sort of bubbling around in the quantum field is precisely the thing that makes space in our models because space is being made by the same kind of stuff that particles are made of and in fact so in a sense space is making the particles the particles are the space and so you don't get to that that means you it's not like the particles are added to the space and then curl it up the particles are making the space and so you don't have that same kind of issue with zero-point energy and so on anyway let me go down and just show you something here this is some about well how big are these things what is the elementary length okay so one thing people have often talked about is thing called the Planck length which is something you get from dimensional analysis in traditional physics and the Planck length is very the Planck length is very is something very involved in what we're talking about but it isn't exactly what we're talking about so we don't have a tremendously good way of estimating the elementary length but we have a possible way of estimating the elementary length and let me tell you how it comes out so in the best estimate we have of the elementary length is that it's 10 to the minus 93 meters now that's really small the Planck length is 10 to the minus 34 meters and so this is really tiny compared to the Planck length actually 10 yeah 10 to the minus 35 meters times this quantity so it's really tiny compared to the Planck length and and roughly the reason that's happening is it's the trade-off between the multi way causal graph and the ordinary causal graph and that the fact that what sort of matters is the multi way causal graph is what's making things be much much smaller than the Planck lengths so that means the elementary time is a 10 to the minus 101 seconds in this estimate and more importantly the elementary energy is 10 to the minus 30 electron volts in the case of the the Planck energy the elementary energy in the Planck sort of way of estimating things is actually 10 to the 19 GeV which corresponds to sort of the energy of a lightning bolt doesn't seem like something very small in the universe when you set this up in this model the elementary energy is 10 to the minus 30 electron volts so that means how many elementary links are there across the universe about 10 to the hundred-and-twenty how many elements are there in the spacial hypergraph about 10 to the 350 so these are big numbers um and you know how many updates has the universe done so far ten to the hundred and nineteen how many individual updating events if you take accounts of all the different quantum degrees of freedom about 10 to the 500 so these are these are big numbers and when woman's worrying about the limit of something you know is what I'm gonna get exactly this is one gonna get exactly continuous space well by the time it's 10 to the 500 events 10 to the 500 is a very very big number and that means that to a very very very good approximation you get continuous space I might say by the way that in the way these models are set up it is possible that the numbers are even much much bigger than that it's possible that there's sort of a continuous some sort of doubling of a continuous sort of increase in the in the number of elements in space that even goes beyond this but with these estimates we can get things like the radius an electron so according to current physics the electron is of zero radius the intrinsic radius of an electron is zero quantum quantum effects produce an effective radius but the intrinsic of radius an electron is zero experimentally we know that the radius of electron must be smaller than 10 to the minus 22 meters in this theory in this particular estimate we're saying that it's 10 to the minus 81 meters across very small um that means though 10 the minus 81 meters is actually quite big compared to the true elementary length of 10 to the minus 93 meters and that means an electron is a big fluffy thing with like 10 to the 35 elements in it and that's why when I talked about particles much lighter than the electron that's why we suspect that those exist because there will be stable structures in the network that are much smaller than something like this okay so one of the consequences of all this is that we can estimate the maximum entanglement speed and the maximum entanglement speed corresponds to about recalling it SATA that's our analog of see the speed of light is Zeta the maximum speed in branch real space and we can estimate that and it's a bit big in this estimate it's about 10 to the 5 solar masses per second I might say that in branch chill space in a first approximation where as distances in physical space relative to times a measure by the speed of light distances in branch chill space a roughly measured by Planck's constant H bar but when you deal with all this multi-way stuff and so on you find out that what really matters is this maximum entanglement rate Zeta and as I say that maximum entanglement rate is is in this estimate pretty big about 10 to the 5 solar masses per second so we at our scale don't usually encounter things that are like 10 to 5 solar masses per second but one can imagine that if for example there was a merger of black holes at the center of galaxies that that would correspond to those kinds of masses doing things in matters of a second and then one would expect that this maximum entanglement speed would have a direct effect on what happens in in in that in that situation and what will produce different physical effects and I might mention that there are other physical consequences of of what we're talking about so for example one that we were looking at just recently is what we can call frame dragging in photons that are in orbit around black holes and that's that we would expect that as a result of the entanglement horizon the correlations between such photons will be different from what you would expect otherwise another there are other kinds of predictions one can make so another one that's that's really bizarre is one of the things we know about the universe is that on a very large scale it's some it has some the Cosmic Microwave Background gives us a sort of a map of what the very early universe well at least a hundred thousand years after the beginning of the universe looked like in terms of where there was mass and where there wasn't mass and presumably that mass eventually seeded the galaxies that the we have in our current universe the question is what did though what made those initial density perturbations well 100,000 years after the beginning of the universe is an awful lot of updates in our spatial hypergraph so we don't really know that we can deduce anything based on sort of early updates in the spatial hypergraph but it's at least fun to think about the possibility that for example sort of breaking of Sentri associated with the very first few updates in the spatial hypergraph might actually have an effect on what we see in the in the Cosmic Microwave Background and I think one of the more science fiction in fact I think because I don't think it's actually going to work this way but we might imagine that that density perturbation is essentially a a shadow of the very first few updates in the spatial hypergraph at the very beginning of the universe and so in effect that that the rule for the universe is kind of painted extremely large on on the whole universe I don't think it's really going to work that way but something like that might might be true um so okay so we're back um me um go and go back here hmm we don't have a visual summary in the navigation okay so I've given you a little bit of a tour of sort of how how things work in this in this model of physics from the underlying rule to all these different possible updates the updates making the spatial hypergraph whose limit corresponds to space the way that the different updates have certain causal relationships and the way those causal relationships define space-time and the way the different kind of foliation of space-time correspond to the reference frames of special relativity and so on and then the way that these that this sort of multi way graph of possible rewriting orders defines the possible the different possibilities in quantum mechanics and then how this branch hill graph of entanglements between quantum states arises and how that how that lets one do the analog of relativity in in sort of quantum in the space of quantum states so I just I wanted to just mention whoops I wanted to just mention so what else can we say I think this is um you know we're we're really I'm really surprised at how far we've been able to get as I said I thought among other things you know ultimately the underlying rule has lots of computational irreducibility associated with it but there's this layer of reducibility that we've discovered that essentially gives us current physics and one thing that should make that not so surprising is that we as observers of the universe succeed in making a coherent picture of what's happening in the universe if we were immediately thrust into computational reducibility that were very hard to do we wouldn't be able to really say much at all about what was going on in the universe so in retrospect it's not surprising that there's a layer of computational reducibility which is essentially what we're keying into when we are sort of perceiving the universe and and and imagining and being able to make sense of what's going on in it okay so I'm gonna mention one more thing that Tim is a little bit of a philosophically complicated thing and which we've worked out less well than we've worked out the rest of what I've been talking about and it's the following question so let's imagine that we finally say great we've managed to find the rule for the universe okay what um you know the question is in a sense why is it that rule and why not another right what what did we you know isn't it weird that we got this rule or not another one for example if it's a simple rule we're in a very strange scientific position because if we look at the infinity of all possible rules most of them won't be simple so to say our universe got a simple rule is to say we're very special in our universe you know ever since Copernicus basically there's been kind of a in science that we're not special our earth isn't at the center of the universe and so on so how come our universe got to be one of the simple universes how come it's that one and not another one and I've been wondering about that for a long time and the really strange thing is that I think we actually have a resolution of that question and it's something that Tim is so here's how it works the so I've talked about how each at every step you can apply different you can apply a particular rule to all these different to make all these different possible updates same rule but there are different ways that rule can be applied in the spatial hypergraph okay so let's go really wild and let's say well we don't just have one rule we have all possible rules and we say not only do we get to apply a particular rule in all possible ways we also get to apply all possible rules that gives us a sort of ultra multi way system a multi way system where the branching is not just four different ways to apply a particular rule but different rules we might apply okay so we've got this giant ultra multi way system so it turns out that it's basically inevitable that in that giant ultra multi way system that we have causal invariants and that means that there is a certain that when we look at the consequences when we look at certain kinds of consequences of this sort of rule of the of the set of all possible rules that will actually end up finding out that we get definite answers for things that are guaranteed by causal and variants and then what what happens is that we can define foliation of this of this rule space basically and in fact well I should say causal invariants in rule space implies a certain rule space relativity and we can define different foliation zuv rule space of this rule of this rule multi way system and what do those correspond to we said that for example different foliation in space-time correspond in the in the in the space-time causal gulf correspond to different states of motion different different foliation x' in the multi way graph and the ordinary multi way graph correspond to different choices of quantum measurement sequences well the the foliation xin in rural space correspond to essentially different forms of description of the universe is getting quite abstract let me let me try and let me try and make a comment about this so when we say we are trying to find the theory for the universe what do we actually mean what we mean in the end is that we are trying to find a way to describe how universe works in a manner that us humans can understand if we just say what does the universe do what we can look at the universe and see what the universe does but to say we want a theory for fundamental physics is to say we want something that we as humans can hold in our hands and sort of understand and find out that does what the universe does now it turns out that I don't think we humans get to do that I think it's it's too far away from what our brains are set up to do but we have a good intermediary and the good intermediary is computers and computation and I think what we're seeing when we are imagining a fundamental theory for physics is we're seeing this kind of three-way situation where on the one hand we've got humans trying to understand things on another hand we've got the the universe just doing the physics that it does and on the third hand I suppose we're dealing with aliens here the we have them kind of this computational this this medium of computation that's a way to sort of that's a place where this process can occur and so I've spent a lot of my life as a language designer designing computational languages to me this is sort of a language design problem can we design a language that can bridge between these three things humans computation and the universe can we design a language that will allow us to describe to make a description across those three different things and essentially what's happening when we look at foliation zuv rule space is we are looking at different possible languages each foliation corresponds to a different description language for for the universe and what this is effectively saying then is that in this kind of ultra multi way system we're saying that the different these different foliation x' correspond to different ways of describing the universe any particular foliation has a particular rule associated with it that will be the rule that we used it works with that description language but another foliation will need a different rule with a different description language that will be the one that it picks as its way to describe the universe so one of the consequences this has is that so we humans have a particular way we choose to describe things we have a particular set of senses we've developed a certain mathematics etc etc etc so we're kind of stuck in one particular foliation it's not the only foliation and we can imagine you know i've i've often you know i've talked about extraterrestrials and things like that and I've often said but at least they'll have the same physics that we do but then I realized it isn't true because they can effectively be operating in a different foliation it's the same underlying sort of universe but it's a different foliation a different description language and that different description language can be not just a little bit different it can be utterly bizarrely incoherently different so that the things that we identify as features of the physical world are just sort of thrown into dust in in in some other foliation which will be which will have a completely different kind of way of looking at the universe so in the end I think that the answer to why this rule or not another is well actually it's all just on us it's because we exist in this particular foliation we explore this particular foliation of this kind of ultra multi-way system and that's that's sort of the experience that we have of the universe and that's when we say we're going to find the fundamental theory of physics it's the one that succeeds in making this three-way connection between our us as humans computation and the actual universe and that's kind of the the goal here so the thing that Tim our the thing we're trying to do then is some that that's so I've sort of given you a sketch of what we know now the problem is can we finish this and can we here let me go back to if I can figure this out okay so so that's that's the story and that's kind of as far as we've got a lot more technical detail very happy to talk about it's all accessible on the on the website we've also made as I mentioned all the tools that we've been using for this investigation available so if you go into for example my technical introduction and you click on any picture there you'll get the Wolfram language code you can just run it in a notebook and you should get the same picture that I got might take some some pictures take a bunch of computer time others do not um but we're we're hoping that this is sort of a foundation on which we can go and try and actually find the rule for the universe so to speak and we can try to understand how all of this connects to the things that already understood in physics I mean I I might say that you know pick some idea like string theory or like twister theory or like causal dynamical triangulations or or like tapas theory or a bunch of other names of mathematical theories which have been developed in physics I thought gosh these are not going to be relevant to the the way that we're thinking about doing physics but I was wrong it seems that lots and lots of these theories are all talking about kind of limits and mathematical analogs of what we're doing and I think that what we learn from those theories is going to be sort of super relevant to to what's being done here and I think that's one of the sort of early efforts is to try and make all these connections between what we've figured out and what people have figured out with a variety of mathematical formalisms and these different kinds of theories I might also say that from the point of view of mathematics this is a very rich hunting ground because we've basically as is unfortunately very typical of physicists we've kind of hacked our way through a lot of fine details of the mathematics to figure out how we can get to answers and when you when you're dealing with limits where the parameter is 10 to the 500 there's a lot of hacking that's okay because that's a very big number um but there's a lot of issues about what really is the multi way causal gough is it really an analog of Twister space is it what is the continuum limit of of each of these things what kind of mathematical structure is it there a lot of very interesting questions there but anyway um so this is this is kind of introduction to what we're trying to do and we're we're planning to livestream a bunch of working sessions that we have about this I would say that in the in the doing of this project which we really started in earnest in about October November of last year that's been a remarkably quick project um we've in the doing of this project we start at some point when it looked like it was actually going to work we said gosh we're having really interesting conversation let's record them so we actually have 430 hours of working sessions that we recorded and we'll be putting those online soon there's also about Tim how many was it it's about 1,200 working notebooks that are sort of the the scratch paper so to speak of this project actually stretching back to 1994 when I really started working on this and we just put all of those online today they should all be the amazing thing as we often language has been nice and compatible so you can actually run those the code from 1994 so um I guess the that's pretty much all I had to say for now and I'm happy to try and answer questions I think um today will probably take mostly more general kinds of questions and people who are going to ask really technical questions probably tomorrow is going to be a better time and I think Jonathan gorod is going to help tomorrow and maybe also today if people ask questions that I don't know the answer to um so let's see I saw I can connect to no virtu two questions here if people have them so as a question here that came a little while ago what is the significance of Planck units in this model I think I kind of answered that the Planck units are set the overall scale but there's an additional quantity that we're calling capital science my favorite obscure Greek letter that essentially represents the parallelize of a multi-way space and that gives results that are numerically very different the the numerically very different from Planck units okay there's a question here do you think this methodology can help us study the emergence of life you know we're very far below things like living systems when we're studying the things that our length scales awarded 10 to the minus 90 meters and so on we're really we're really deep deep down in the in the sort of the micro machine code of physics so there's a there's a pretty long way from that to living systems having said that the mathematical structures that have emerged in this model of physics turn out to be as is often the case if you have a sufficiently simple model it's going to be applicable for lots of things and I actually think it is going to be applicable to a bunch of questions having nothing to do with its application of physics just the mathematical structures that we built I think are going to wind up being applicable in a lot of other places and I think one of the places is actually possibly to a theory of evolution I think that that rule space relativity thing that I was talking about might actually have quite a lot to do with that when you look at these different possible rules that's a bit like looking at the different possible genomes that can exist and so there may be a essentially mathematical not not structural but just mathematical analogy between what we're seeing in physics and what we're seeing as a sort of a doable theory of evolution that's one thing I mean even more bizarrely we were looking as part of kind of helping with endemic issues we were looking at digital contact tracing and we realized that the reconstruction of essentially if you know just the whose phone interacted with whose phone that kind of gives you elements in a causal graph and the reconstruction of space-time which is kind of who was where when from the causal graph of whose phone interacted with whose phone is bizarrely similar again to the mathematics of what happens in this theory of physics so I think that we're going to see a bunch of applications of the structural theory here in addition to applications to actual fundamental physics itself and I might mention also that what we're doing here is essentially a big story of parallel computing I mean essentially what's happening is that in the operation of the universe so to speak we are saying there's a vastly parallel computation going on fact one of the things that probably held me up from doing this project for for a while was I just couldn't believe that the universe was such a profligate waster of computation as it seems it actually is with all of these different paths being followed and so on but that following of all those different parts is really a story that's like parallel computation and in fact this notion of Koslow invariants these ideas of foliation and so on these I think are potentially very applicable to approaches to parallel computation and I think there will be a very interesting interplay between what one learns I mean the the the causal graph is a partially ordered set and what one is essentially doing it's like the universe is doing a breadth-first search and respecting this partial ordering of the partially ordered set and you can think of it in a very computational way like that I mean in a rather bizarre sense the universe is like evaluating an expression and the whole operation the whole history of the universe is the evaluation of an expression if you think about it in terms of lambda expressions there are the free variables of lambdas and essentially everything in our universe is a bunch of escaped free variables from lambdas and this in this in this picture okay let's keep going here um ah how long does this project spend I'm not sure quite what that word means there will the work be published after peer reviewing well yeah we we I mean this is we're just putting this out today and it'll the my giant 450 page document will let's say I hope lots of people read it I hope lots of peer reviewers read it um and then it will appear Jonathan's some Jonathan's papers as I say uh are much more suitable for equation first readers and they will go through that same process this is a it's a it's a fairly complicated conceptual structure that we built here and it might take a little while to get to get well absorbed um okay what is a node and what is a line here so okay so what we're thinking about is tend to call them elements and relations the the nodes are just abstract elements the only thing we know about them is that they exist and that they are distinct from each other those are the only things we know about them we can call them one two three we can call them XYZ we can plot them as points on a picture do all kinds of things but all we really know about them is that they are distinct things that exist okay the lines are relations they're saying these elements are somehow related and a hyper edge like a ternary hyper edge would be a relation between three of those elements and the way this model is set up in detail the order of those elements matters in the relations probably doesn't need to be work that way but that's the way we're doing it it's very general so that's that's what it is it's just elements and relations now we can represent the elements and relations if if the relations are just binary relations that's what happens in a graph where there are nodes in a graph and the nodes in the graph are connected by edges and there are node at each end of the edge that's like a binary relation that's how we build up the graph but as far as we're concerned they're just elements and relations they don't have that that's that's what everything is made of but it isn't really a thing that we can talk about beyond just saying it's these elements and relations um you have a path for replicating the laws of thermodynamics yeah actually I think I figured out the laws of thermodynamics and in the 1990s um his how it works the so the main thing that's mysterious so that the second law of thermodynamics is the big one to worry about it's the law of entropy increase it's the law that says when that typically you that what starts is very orderly like motion of molecules eventually turns into very disorderly motion of molecules that's that we call heat you start off from some very structured order ordered thing molecules bounce around the molecules eventually arranged themselves in a sort of way that seems completely random so people had for a long time so back in the 1870s I think Boltzmann proved this thing called eh theorem that says you can based on looking at microscopic collisions of molecules you can show that entropy increases problem with that was you also showed that entropy decreases because the way that we believe microscopic laws work is for all practical purposes for what matters for these the laws are are reversible in the sense that any collision that can happen forwards in time can also happen backwards in time small footnote to that but it's not relevant for the duration of thermodynamics um okay so there's microscopic reversibility but macroscopically once stuff is turned into heat it never goes back from heat spontaneously once you've got that kind of randomness you never spontaneously get order again how can that work well actually it's and it was really quite unclear that worked I think in the end let me see if I can pull up a something to show here hold on one second if I can work this properly it's hard I am not seeing what I would expect to see in my thing here well maybe maybe I go there okay all right show you um something about this um this is my big book there's a section on irreversibility and second law of thermodynamics and the main thing to understand is some that you can have even a reversible system and what happens is at some point it may have a simple beer maybe in a simple state but just as a result of kind of the computational irreducibility of the evolution the thing will effectively encrypt that initial state into something that looks for all practical purposes random so the origin of the second law is essentially that as observers with bounded computational capability we see things going from lower entropy more ordered States to higher entropy disordered States so essentially the second law of thermodynamics is a consequence of the computational boundedness of observers in in the physical world and that's how it works I think and for purposes in that way of setting things up that's important in this theory of physics because it's what it's what allows us to take these continuum limits to get ordinary space-time and things like that but a quite separate thing is that I think that the origin of the second law is essentially computational irreducibility that is leading to essentially the encryption of initial conditions for purposes of computationally bounded observers see here okay about can you talk more about the relationship between physical particles virtual particles and space itself so I think what we're really when we're talking about particles let me let me show you another example which I can also find in the uncursed buck I think um let's see where they are here's a good example yeah so this is this is that rule 110 cellular automaton that I was showing you and this is just an analogy in the case of spatial hypergraphs it's more complicated but here we get to sort of just lay the particles out we already know how to lay the particles out in space-time so here are some particles that are propagating around and this is you know these are particle collisions here these are two particles colliding making another particle so a typical you know we can sort of catalog the particles here's a bunch of particles that we can catalog and when those particles propagate for an infinite time that's like a real particle like an electron in the language of particle physics and on it's on the mass shell of their own shell particle that has some that has a you know physics p squared equals m squared the for momentum squared equal the mass squared something where the particle can propagate without making use of kind of quantum mechanics to exist now in quantum field theory there's this notion of virtual particles particles that exist only for a short time that sort of our the uncertainty principle for particles makes that possible and virtual particles rely on quantum mechanics to exist and virtual particles are in in this we don't know all the details of how that works in in our models but roughly what's going to be happening is that those are particles that don't propagate forever in the special hypergraph and not only that they also are particles that have sort of an entanglement in the branch field direction and so they are there they're virtual particles that exist as as things that are not sort of completely mind in they don't have they don't have an absolutely definite structure they have a structure that sort of extends in Branch Hill space and can last only a certain amount of time in in physical space and in space-time and that's that's sort of the the rough picture of how of how the virtual particles work but we have more to figure out there in fact one of the first live students will probably do is probably talking about quantum spin and talking about so that's sort of one of the pieces of what we need to understand how particles work and we'll talk about thing called the spin statistics theorem we don't yet know how to derive it that's why we're you know that's why we're going to try and figure it out and that will be related to a bunch of these questions about how particles work um and so the question of the relation to space is these are just like you can see this sort of background of pattern here that's sort of the space in this very simple cellular automaton and the particles are just following exactly the same rules as the background space but they have this localized form and it's the same kind of thing we think in the spatial hypergraph but the background space is something more random essentially what what these particles will be is a sort of topologically stable structure in this background space so just like their little vortices and water that you can see that have a certain stability to them not affected by even for example some turbulence in the water so similarly here there will be some kind of topological structure although it isn't actually topology in the ordinary sense of topology because we don't have certain data we only have this connectivity data we don't have more data about faces and things that you need to form ordinary topology but it's something analogous to topology um ok oh I might mention another thing which is you might ask the question all these particles running around in space how important is that to space well I think that all of the real particles that is the virtual particles a different story but all the real particles in the universe might represent one part in ten to the hundred and twenty of what's actually happening in the spacial hypergraphs so in other words everything we know about particles the vast majority it's a tiny little piece of fluff on top of all of this activity which is basically maintaining the structure of space so you know ten to the hundred and twenty you know things maintaining the structure of space relative to one thing doing something with the particle so that kind of gives you a sense most of the activity of the universe in this kind of set up and with this estimate of parameters is is involved in the maintenance of space and the existence of particles is just a small little twiddle on top of that okay let's see um okay if we find the model for the universe and run the code would it be computationally equivalent or actually equivalent to something like the Big Bang yes absolutely if you if you get if we get sort of a final rule and we know its final initial conditions by the way you don't really have to distinguish between rules and initial conditions you can always build the initial conditions that's part of the rule um if we if we have that and we just run it and we run this giant multi way graph according to this theory we will get everything in our universe um and that's that's um that's that's what we get to have and and sort of the expansion of the universe is then associated with the expansion of this of this spatial hydrograph and so on okay question from Justin here what predictions have you made that you think will be easiest to verify empirically um one of the okay so the first thing is in a sense theoretical verification what do I mean by that well there are emerging studies of things like black holes and so on that have made various inferences that are non-trivial inferences from existing physical theories the fact that we can directly get to those inferences from this theory is significant now anything to do with black holes is going to be somewhat theoretical we know from from gravitational wave detection that that we know some features of black holes but but by the time we're talking about sort of quantum effects around black holes that's theoretical but already there are theoretical predictions that can be verified in the context of the theories that have been being developed in the last few decades around those kinds of things so that's first first type of thing um the second the second type of thing is well being able to is kind of things like these ala ganas these very light particles we don't know exactly what their mass will be but the the kind of the strong suggestion from these models is very light particles are very likely to exist similarly some of these things about the early universe similarly this maximum entanglement speed we just don't know the numerical value you know is it exactly ten to the five solar masses per second or is it ten to the four solar masses ten to the six solar masses per second we don't know exactly um and to really know that for sure we kind of have to find the actual rule but we can already there's a suggestion of things to look for even though we can't nail down the actual parameter and as I mentioned things like these correlations in in photons orbiting black holes things like that my guess is there are also things to be looked at in quantum computing this this theory has definite implications for quantum computing it has more theoretical implications than about what's in principle possible in quantum computing cause low invariance implies certain limits on what's possible in quantum computing and this maximum entanglement speed does also but the those things may be far away from what's experimental II accessible or it may be possible to very cleverly arrange things in quantum computing so that you can actually see some of these effects like maximum entanglement speed I'm not sure yet um I think that's that's going to be a bunch of hard work figuring out the details of what those predictions might look like once you know if we can find a definite rule then then it's really going to be much easier to get very definite predictions because we're going to know the exact scales for things and so on right I would say in terms of finding the rule there probably five attributes that we think the final rule has to have among them you know giving eventually three-dimensional space having certain properties about causal invariants and so on um we have rules individual rules that have each of those probably five attributes but we don't have a single rule that has all of those attributes and it's a question of finding that I mean actually you know I think I mentioned before that we have this some registry let me show you this we have this see this registry am i sharing my screen yes I am we have this registry of notable universes and you'll see here um let's see this was some some computed properties of this particular universe you know the embarrassing thing is it could be that in our register you already have our physical universe with our description language but we don't know that yet um so but this is something we have to we have to go explore um ok it's a question about the renormalization group and this framework I think the internalization group is alive and well in this framework I think how about we do that if we want to talk more about the realization group let's talk about it tomorrow and our physicists and mathematicians Q&A because I think that's gonna get fairly technical fairly quickly um thoughts about Leonard Susskind ideas around entanglement complexity let's see is Jonathan online here maybe Jonathan would like to take that some yeah I'm here if you go ahead you want it do you want to you you you read these papers much more than I do right right so so it turns out that actually the the geometry that's induced on branch eel space as Stephen was talking about it seems to be remarkably similar to a lot of the geometrical ideas that that Susskind has been talking about in the context of things like the ER equals EPR conjecture and stuff like that and so so one possibility is that well okay so effectively what happens is that different points in branch real space their natural distance metric is expressible in terms of something like an entanglement entropy and then things like the ER equals EPR conjecture which is what Susskind is interested in can then be formulated about in terms of correspondences between the multi way evolution graph and the multi way causal graph but as Stephen said earlier we should probably address this in more detail and Alex well we'll talk about it in full technical detail right right but the short answer is yes it's definitely related then okay next questions about string theory um and the question is is this related to string theory we don't know for sure yet you know I was writing my sort of technical introduction to this stuff and I wanted to talk about the analogy with string substitution systems and I was thinking about the title of that section being you know the case of strings and I thought oh my god is gonna confuse every physicist because they'll think I'm talking about string theory um and then I started thinking well actually is there an analogy but between these string substitution systems in string theory and you know it's kind of starts as a pun that the if you make these strings longer longer and longer and you're kind of looking at the continuum limit of an infinite number of symbols and the strings what is that theory and the absolutely bizarre thing is that that pun may turn into physics it may turn out that the continuum limit of string substitution systems is string theory or more accurately string field theory we don't know that for sure yet but that's an interesting possibility and it's something that well I hope some string theorists will we'll get into looking at that and looking at how the analogy between what's happening in this in this theory and in string theory my guess is that string theory is a kind of is will end up being sort of a simplified limit of some part of this theory that would be my guess they don't know that for sure yet and possibly even this limit of these string substitution systems which actually aren't the same as as spatial hypergraphs spatial hybrid graphs are in a sense much cleaner and have much less intrinsic structure than strings do they don't yet have a notion of ordering and things like that in them but that's that's my at least my guess right now for how that might correspond um can this model explain weak nuclear forces so the answer is it's certainly better the the thing that we know that the weak nuclear force is associated with the su 2 cross u 1 local gauge invariance that exists in in physical world and there's a question here of so local gauge invariance is kind of like we can think of sort of rotation invariants as things are the same when you kind of rotate what the laws of physics are the same independent of which way you're rotated so to speak and there's a more local version of that that sort of you can rotate locally and have it be the case that you can match things up in such a way that you still get the same laws of physics there's an analogy of that in rotating in kind of an internal space that corresponds to the space of the so-called gauge groups and actually in in our models there is I think we very strongly suspect that local gauge invariance can arise rather easily in our models and essentially the way it arises is that when you're doing updates when you're applying these updates in different term you can apply these updates in different ways at a particular place in the spatial hypergraph and these there are multiple ways of applying these updates that essentially correspond to sort of a rotation in the spatial hypergraph and that rotation in the spatial hypergraph is like the operations in the gauge group and when you kind of look at successions of those things we think that the limit of the kind of equivalences between different updates that the limits of that set of equivalences will correspond to the lis group continuous group that corresponds to a local gauge group so just as the limiting of the spatial hypergraph itself is to a manifold something like ordinary space the guess is that the limiting of local rewrite rules around a particular point in the spatial hypergraph will end up corresponding that the limit of those things will end up corresponding to a lis group that will correspond to local gauge invariants in the system and that that will be what leads to the knowing local gauge invariants and you know it's part of su 2 cross V 1 is what gives you the W boson and Z boson and the weak nuclear forces and you know I have to tell you when I was a kid the weak nuclear force was my favorite thing and I even when I was about 13 years old I wrote this book length description of weak interactions that was all about that so that was that was before gauge groups were really much of a thing but I'm a super big enthusiast of the of the weak interaction in physics and it's but but actually we've we can already leverage what's been done in the standard model of particle physics to know that if we can get the standard model we've got weak interactions lets you do all generative rules produce curvature like objects in an emergent way so the issue is what is curvature and what is dimension that's really the big part of the story so we talked about measuring dimension by looking at the growth rate of these balls in in the spatial hypergraph curvature is and so dimension is kind of leading term is the exponent of the leading term in that growth rate curvature is a correction to that so for example it's R to the D times 1 minus R squared times the Ricci scalar curvature over 6 plus D plus 6 times D plus 2 and so on but in other words the the existence of curvature changes the rate of growth of the number of elements in these in these so-called Gd SiC balls and so it's a complicated interplay between curvature and dimension once you say there's going to be finite dimension then all the corrections to that once you fix the dimension the corrections correspond to culture exactly what the interplay between curvature and dimension may be there may be some slight surprises there in terms of of sort of things that are mixtures of dimension of curvature which we don't understand yet because all the calculus we have built is in integer dimensional space we don't really know what the analog of curvature is in fractional dimensional space and that's what we have to be able to understand and to understand that interplay let's see is there an equivalent graph with unordered edges to a given graph with ordered edges yes there is I talked about that in one section of my technical introduction the actually the stuff I was studying the 1990s involved unordered graphs rather than rather than these ordered hyper graph constructs and the frustrating thing is at the end of the day after we do all of this work with all this very elegant system with elements and relations and so on essentially you can get the exact same results with trivalent graphs the only thing that's different is the enumeration of rules is different so if you say I want to find a simple rule that does this or that the the the order in which you may enumerate those rules may be completely different for trivalent graphs as it is for these ordered hyper graphs so there is a difference there and I think the ordered hyper graphs are sort of a cleaner way to enumerate what's going on but it's sort of a consequence of having models which have sort of computation in a solitude that they all eventually end up being in some sense equivalent to each other and the frustrating thing is I was super close to figuring this out in the 1990s but you know I I I should have pushed a bit harder to get there but um but I didn't and so the sort of languished for many years um okay let's see okay so there's a question from Steve here on the live stream about a destructor that so I've been talking a little bit most of the time I've been talking about a single rule being applied at a time where a single rule being applicable where that rule increases the size of the hyper graph you can absolutely also have rules that decrease the size of the hyper graph and yes you can have a dynamic equilibrium between rules that are increasing size of hyper graph and decreasing the size of the hyper graph I don't know whether that's going to end up being important I'll tell you a kind of a an allegory or something when Einstein invented the Einstein equations for general activity in 1915 one of the things that the most simple-minded equations he wrote down predicted is that the universe expands and he said but of course the universe isn't expanding we can see that we know that so I'm going to add this thing called the cosmological term to fix that problem that the universe would be expanding according to his equations and he later said the cosmological term was the biggest mistake of his life so to speak that because it turned out another fifteen year later it turned out well actually the universe is expanding now we there's a lot of discussion about how big the cosmological term really is and we now think there might be a cosmological term long complicated story related to virtual particles and zero-point energy and so on but um so in in the in general Attila T Einstein made this mistake of saying well the natural thing is that space expands the universe expands but I'm gonna put this hack in there to prevent it expanding so I'm trying to avoid making the exact same mistake it is certainly possible to have in these rules dynamic equilibrium where you have sort of a limited rate of expansion because there's also contraction or you can have rules that just unbounded Li expand I don't know what's actually right and we need to look at that um but I think to say well we obviously need rules that decrease the size is kind of making exactly Einstein's mistake and I don't want to do that so could this answer the mystery of dark energy and dark matter so I mentioned dark matter my best guess is that these things I'm calling all Egan's these very light particles much lighter than the electron could be related to dark matter the main issue with elegans is the question of how hot are they how fast are they going are they going slow enough that they'll be caught in the gravity wells of galaxies and things or not that's a question of essentially if polygons were produced in the very early universe how do they do they get to the point where they interact only so weakly that they only feel the force of gravity they don't feel any other forces and as a result as the universe expands they effectively cooled down now particularly if they were produced at a time before the dimensionality of space ended up being 3 and before we had kind of the inflationary period in the in the evolution of the universe I think there is good reason to think that they will be very very cold but there'll be very low energy and that therefore they will be caused from the gravity worlds of galaxies which means that they are reasonable candidates for dark matter now their their interaction with anything other than gravity would be extremely weak and so that's a challenge in terms of detecting them and that's one of the questions is is whether one can can make specific models and try and do experiments around that dark energy is a little bit of a different story that has to do with acceleration in the expansion of the universe and that I think is more to do with if it exists and if that really is acceleration really pans out in that way is more a story of the exact structure of this some of the way the spatial hypergraph works and effectively in the derivation like jonathan has a nice derivation of Einstein's equations in which essentially the cosmological constant which is what leads to dark energy and so on Rises is a constant of integration in in certain equations and so we can't determine from our most immediate derivation what that constant of integration is when we have more knowledge about what the underlying rule is we should be able to determine that and that will tell us whether whether this sort of spatial hypergraph whether the structure of the spatial hyper graph can add a dark energy term to the Einstein equations um so next question is what does this tell us about the nature of time and is there physics to it well in these models time is essentially associated with this sort of inexorable upper doing of computation so the universe progresses through all of these different rules being applied and it is the aggregate of the progression of the application of those rules that is the passage of time and one thing to mention is that in in ordinary physics there are several different kinds of time there's cosmological time the time that defines the expansion of the universe there's kind of thermodynamic time the time that defines the integration of entropy and the formation of heat and so on there's perhaps psychological time for us humans perceiving what's happening in the universe in this model one of the nice things is that all those kinds of time are aligned and they have to be aligned because they're all associated with this underlying kind of computational process now what happens is we know a lot about how time works and based I'm your artillery and so on what happens as I was talking about before is that in these models the all of that sort of structure emerges as a consequence of the sort of large-scale operation of the model well what you put into the model is time as computation what comes out of the model is time in space time time as it operates in quantum mechanics time in the ways that we're familiar with it in physics but what time is in these models is computation of the program that the passage of time is the operation of irreducible computation and it's kind of a satisfying answer because it means that as time happens something irreducible is going on it's not like we can look at our universe and just say oh you don't need to run the universe you don't need to exist for all these billions of years we can just jump to the end and the answer is 42 or something um the what this is saying is in this model we're explaining no actually you can't do that there's irreducible computation involved in the progression of the universe that's what time is is this irreducible progression of computation and in a sense that irreducible progression of computation really means something it can't be done any way than to just actually run the universe and see what it does we can't kind of jump ahead and immediately say this is what the outcome is going to be how confident are we that will find the rule it's a good question you know last fall when we restarted doing this project I didn't think we'd get anything like as far as we've got I thought that we will be slammed into computational irreducibility almost immediately that we will be looking at you know maybe we can get the first 10 to the minus 100 seconds in the evolution of the universe but we'll not know whether it really connects to the universe as it exists today it's worked a lot better than I expected because there's this layer of computational reusability that we've discovered in these in these models now searching for the rule the rule that corresponds to our description language and so on I don't know how hard that's going to be I really don't know and I don't know whether you know I I was going to I don't know whether we're going to find it this month this year the century um it is not easy to predict that because we just don't know whether essentially what the question is how good a description language is what I've been telling you today how close is this to aligning between us humans the physical universe and computation as we know it how how successful have we been at aligning those things if we're successful enough the rule is going to turn out to be something very simple expressed in that language um and we just don't know how successful we are at doing that and so we just don't can't tell how hard it's going to be to find the rule I mean we're going to be doing all kinds of searches for it hopefully other people will as well it's not trivial to set up criteria one of the things that happens in searching the sort of computational universe of possible rules my little mantra is the computational animals are always smarter than you are anytime you set a trap for them anytime you say I'm gonna use this criterion to decide which ones are interesting you'll find ones that somehow manage to squiggle around that trap they do things that you absolutely didn't expect and so it's a little bit difficult doing these systematic searches but you know we'll do a bunch of these and hopefully other people will will help in doing that and that will help in homing things down and then we'll have to do a bunch of thinking about it let's see can we talk about emergent effective differential geometry from fundamental computational rules absolutely absolutely the the differential geometry that emerges from that that's exactly what we're doing we're saying when there is a finite dimensional space that emerges it has certain properties that have certain differential geometric features that happen to correspond to Einstein's equations when you happen to end up with something whose limit is integer dimensional space you can go to town with differential with traditional differential geometry you can define Riemann tensor as you can talk about Christoffel symbols you can look at you know equations of deviation all these all these things they all just work they are more elaborate and less well defined in fractional dimensional spaces that's kind of a math thing that still needs to be figured out let's see a standard sci fi question can you go faster the light is time travel possible okay um they can you go fast and light complicated because in branch real space you're reaching that's a slightly complicated thing you can have entanglement like you're doing quantum mechanics but the light cone is sum and depending on how how wild the structure of space-time is you can have wild wormholes and things like this but they'll work in pretty much the same way as they do in general relativity I think the that's that's story the story on faster than light travel is it's kind of going to be the same as general relativity a story on on time travel closed timelike curves is yeah you can you can have rules that give closed timelike curves and the multi-way graph for example but those rules do not admit the possibility of foliation z-- that are kind of consistent time foliation z-- so again closed timelike curves end up being like a consistency condition between different parts of the system and they have a sort of trouble in terms of well they have trouble for causal invariants they have essentially cause on variance says you can't have closed timelike curves um and so so you don't get but time travel is a messy concept anyway and the basic answer is you can't have it in these in these kinds of models antimatter problems so the question so one question about the universe is there's matter and as antimatter by the way we don't yet know in our model how antimatter works to every particle there's you can apply to every particle this operation of charge conjugation that goes from a particle like an electron to its antiparticle the positron and there's a question of how that will work in these models we don't know that for sure the first thing we expect we would get is a thing called the cpt theorem which says that if you do charge conjugation parity that space inversion and time reversal that the result of all those three things is guaranteed to in in traditional physics Lorentz invariants relativistic invariance guarantees that cpt invariance is an invariance of any theory we haven't shown that yet in our theory but I don't expect it to be that difficult to show that and that will at least give us some hint about what what how anti particles work and how one gets actually actually as I think about it I have an idea for how that might work which I haven't thought about yet see we've been in the last few weeks as we've been sort of preparing this for to be able to present things and website and so on we've had kind of a no science policy because we know that if we start doing more science there will be a never-ending process to get to the to get to the end it actually reminds me of Zeno's paradox and I have to mention something I had forgot to mention I was talking about it I mentioned time dilation in relativity relativistic time dilation it turns out there's a similar phenomenon in quantum mechanics it's called the quantum Zeno effect that basically says if you measure too often you won't see things change so essentially time is dilated if you make too many measurements and in our theory that's very beautifully comes out it basically says as you move in Branchville space that motion and branch field space gives you a time dilation and that is the quantum Zeno effect but anyway we were worried about a Zeno effect for this project where if we do too much science if we just keep doing the science will never end the project so to speak so anyway one of the things we should talk about is charge conjugation and I just had an idea of how that might work so and I think the but about antimatter in general one of the mysteries of the universe is that there doesn't seem to be much antimatter in the current universe there see it seems like there's and we might have thought that in the early universe it will be symmetrical between matter and antimatter actually I worked on that problem back in 1980 trying to figure out why there's more matter than antimatter in the universe and with we came up with a definite theory about that which we don't yet know whether it's right or wrong because it involves some particles much heavier than things we've been able to see so far the the core phenomenon that leads to the possibility of matter compared to antimatter is violation of CP invariants so the the universe is seems to be invariant with respect to rotations for example but if you do a space inversion if you just negate all the coordinates so-called parity transformation the universe is not invariant under that the weak interactions for example well actually the the most obvious thing is neutrinos are every every neutrino is almost exactly left-handed in the sense that it is its direction of motion and it's its spin is always arranged in a kind of left-handed way with respect to its direction of motion and that means that space inversion the universe is not symmetric under space inversion and the universe is also so I mentioned universe is invariant under the combination of charge conjugation parity that space inversion and time reversal it seems to be invariant under that but individually it's not invariant under any of those and it's also not invariant under CPE charge conjugation and parity or equivalently under time reversal and that in equivalence is at least in the theory that I talked about around 1980 that is what leads to an excess of matter or antimatter when you combine it with the expansion of the universe but we don't know how that's going to work in our models and for example there's a small amount of CP violation that is observed in particle physics and being able to reproduce that and our models will be really cool don't yet know for sure how to do that we may or may not have to actually start constructing things that represent particles like quarks and so on to be able to get that or it may be something more generic I kind of have a slight suspicion it might be more generic which makes it makes it possible to kind of figure it out without knowing the ultimate rule let's see here's the model consistent with the ever at Ian multi worlds theory how about we we send that one to Jonathon here you want to Jonathan do you want to take that yeah sure okay so the answer is it essentially is so the this whole notion of multi way evolution the way we've constructed it and it's connection that we conjecture it has with quantum mechanics is very reminiscent of the many-worlds interpretation of quantum mechanics so the the sort of the the simplest version of the ever rezian interpretation where you have non interacting branches of quantum evolution that effectively corresponds to the to the special case in which you have just a multi-way evolution graph where everything is branching and you get no convergence between states in the more sophisticated kind of Doshi and version of the of the interpretation where you get interaction between parallel branches of evolution history that corresponds to our notion of kind of multi way merging and this notion that Stephen was talking about earlier of sort of of walling off states within within sort of event horizons of quantum observation frames and things that there's more detail we can give but we should probably save that for tomorrow okay question from David here are we saying that the universe is deterministic the answer that is simple the answer is yes um however it's a little bit more nuanced because we're saying that there is this multi way graph that has all of these different evolution histories but we as observers of that graph are basically slicing across different ones of these histories but the the ultimate complete multi way graph is absolutely deterministic the our perception of it may not seem deterministic but the actual progress of all those possible branches is completely deterministic if you ask questions like okay what does that mean for free will well that's all about computational irreducibility computational irreducibility is what gives us a an impression of free will because even though everything is determined you can't know what's going to happen effectively more efficiently than just running it by running the computation so you can't know oh it's it's not like you know the the the 1950s style robot science fiction thing where like the thing operates according to logical rules and therefore you can predict what it's going to do doesn't work that way because of computational irreducibility one is sort of stuck having to just follow the progress of time to know what's going to happen how do you measure if the rules one has are successful that's a good question and that depends on this whole computational irreducibility versus computational reducibility question in other words the you know the ultimate question is do we reproduce the parameters we know in the universe do we reproduce that there are three dimensions of space do we reproduce that the muon electron mass ratio is 206 do we reproduce that neutrinos are primarily left-handed all those kinds of things um that's that's what will ultimately determine whether we found the rule but we can already say so it is one thing if the rule is simple then as soon as we get three dimensions of space and you know electrons and and electrons and muons and Torr lap tones and things I would be amazed if it wasn't actually the rule because the distance between one simple rule and the neighboring simple rule will be huge with respect to its effect on the universe so going from one rule to the sort of nearest neighbor rule you'll go from three dimensional space to you know infinite exponential space to something you know wildly different so as soon as you've got the basic parameters of the universe you can be really I think very confident that everything else is going to fall into place but so that's that's the best hope and and how difficult it will be in which parameters we will find first I don't know for example I have a suspicion that the local gauge group is going to be a direct window into the underlying rule that's going to constrain the underlying rule a lot in a way that I think that the dimension of space does not I think the dimension of spaces is emergent over to larger a scale in space and time to be as useful I suspect the local gauge group will be much better constraint but we'll have to see ah do we see the possibility of new ways to manipulate space oh that's a good question I don't know I mean of course all of these things are operating at lengths scales of like 10 to the minus 93 meters that's incredibly far away from from what we have right now you know if you've got a pet black hole in your backyard then there's a lot more you can do but we don't have any pet black holes probably for the better um the the question of whether by doing some kind of quantum measurement process and by doing some iterative quantum measurement process you could have some some strange effect through this whole branch field space thing it's conceivable it's conceivable there might be some way to kind of sort of slide teleport through space in some elaborate way by making use of some feature of branchial space I don't know right now it seems far away but I'm not sure I mean it's worth remembering that in particle physics we still don't have a single sort of practical application of anything beyond the ordinary particles we don't there's no strange particles for example which are particles whatever there's nothing yet that's been sort of reduced to to practice even relativity the you know that's a hundred years old we're still only at the very beginning of of having things which really where relativity really matters in practical in directly matters in sort of practical things we measure used in engineering and so on lagoon's and neutrinos how much lights are the neutrinos will they be well we don't know we know the neutrino mass matrix we know we don't know the individual rest mass of neutrinos but we know that neutrinos mixing with other neutrinos have certain rates the I'm trying to remember the bounds on neutrino masses right now I'm I'm the the point is that we're still we've got kind of 30 orders of magnitude between the absolute minimum masses of particles because there's an elementary another thing I should say you know in standard physics right now space and time are continuous and energy is also continuous and mass is also continuous there's no quantization of mass and energy and space and time this quantization of angular momentum there's quantization of all kinds of other things but there isn't quantization of space time energy momentum and mass in these models those things are quantized but the individual quantum units are really tiny and the point is that I'm sort of guessing that you can have particles that are a small number of quantum units of mass and those are really really tiny twenty or thirty orders of magnitude smaller than current bounds on neutrino masses so but that doesn't mean that there couldn't be a whole spectrum of particles that live in that space so much lighter than neutrinos so much lighter than all these other kinds of things I mean neutrinos have very weak interactions that's part of why they have low masses but there may be other reasons it's kind of complicated is not directly connected to that the it but you know this possibility which really had never occurred to me at least that there might be you know 20 orders of magnitude or 30 orders of magnitude of lighter particles I've never really considered and I think that's a that's that's an interesting kind of thing even when we don't know the full parameters to start considering next one how is the graph stored 10 to the 500 steps requires a fair amount of memory yeah it requires all the memory in the universe it is the universe I mean this is one of the kind of philosophical questions that comes up when you start saying the universe operates according to a rule it's a kind of computational rule people start saying well what's that rule running on you know where's the computer that's running this rule well it doesn't work that way the rule is just a description of how the universe works it's like when we know that the motion of planets is governed by differential equations we don't think that the planets have little mathematical inside them solving those differential equations we're merely saying the differential equations are a way of describing how the planets move and it's the exact same thing here we're saying these rules are a way of describing what the universe does the universe is equivalent to performing these computations it's not that the universe somehow is externally performing these computations it's just the actual stuff the universe is is the performance of these computations and so that that means the the data structure of the universe is the universe the computer of the universe is the universe itself it's it's running itself so to speak and and by the way I mean it's it's it's interesting to kind of see all these things about computation all these ideas about computation like trade-offs between space and time and computation that's actually physics the trade-off between space and time is related to relativity and like turns and things like this the question of I mean you you've you know by by turning what one has done in a theory like this is once conflated three things once conflated computation physics and mathematics they're really ultimately all the same kind of thing so you know mathematics is something where you start off with sort of axioms and then you say well what are the deductions you can make from that physics has always been this empirical theory where you say well the world roughly works like this and this is an approximation but this is saying that we can actually find the rule the precise thing like an axe in mathematics where just by working out the consequences of that rule just like we work out the accident of mathematics we know precisely what the universe does of course this computational reducibility so it's irreducibly hard to actually do it but from a conceptual point of view this will reduce physics to mathematics and similarly in a sense it's reducing physics to computation and it's providing kind of a and we can actually think about computation then that this is the universe is just an example of a parallel computation and the laws of physics will also be laws that apply to these parallel computations and so we can start talking about sort of relativistic things and I haven't figured out yet this is another good thing we should we should talk about is the analog of time dilation for space-time trade-offs in in in parallel computing but I think all of that formalism will be able to be interconverted they're um are there any applications of this in the near term for an average person my theory is there are no average people but but anyway the its some here's the way I think about that the you know is there going to be technology that operates on the basis of elementary lengths of 10 to the minus 93 meters not anytime soon um I think the the main significance of this is probably a conceptual one I mean I I would say that you can sort of draw a slight analogy to you know like what Copernicus did in um back in 1500 or so you know people had always thought you know the Sun goes around the earth all those kinds of things there was this whole theory of you know ptolemies theory of epicycles all those kinds of things work just fine for predicting motion of planets even today when we you know work out what an eclipse is going to happen we're basically using the computational analog of tens of thousands of epicycles but what Copernicus did was he showed that actually there was a mathematical theory that you could set up that didn't follow what we sort of perceived from our senses that the earth is stationary and the Sun is moving around it but that actually said well no that's not really the case this mathematical theory shows that you can have the Sun at rest and the earth moving around it but the theory was kind of complicated and it had a lot of technical detail and you know I don't know how many people cared about the theory but the consequence of the theory was that the the science and math can tell you things that weren't obvious from everyday sentient from your from your ordinary senses and that started a huge progression of kind of scientific thinking that said just work out the science don't um the fact that you can't figure it out by pure thought by just pure reasoning isn't really the important thing science can figure it out well I think what we're seeing here is that we're sort of seeing a foundation for physics for our understanding of the physical world that's rooted in computation and once we really believe in the fact that computation is what it's all about once we really believe it all computation kind of all the way down that has consequences and so for example one of its important consequences is the phenomenon of computational irreducibility you simply can't get out of computational irreducibility once things are computational you will have computational irreducibility and computational irreducibility has everyday consequences it's the thing that tells you you can't just figure out what's going to happen in with by by just sort of pure thought it's the thing that tells you you can't know whether a program is going to have a bug in it without running it it's the thing that tells you when you have an algorithm for deciding what what content should be in a news feed and some some AI based algorithm for that you can't know what its consequences will be without effectively running it it's the thing that kind of limits the the effectiveness of science to make a sort of global predictions it's it's a way that science it's sort of interesting that that term for example in the Copernican case that that was kind of just trust the science it's going to figure everything out what we're saying is when things are rooted in computation there are inevitable limitations of science that come about just by the nature just by the logical structure of the way that science is built from computation and those central around computational irreducibility and those implies certain limits on the way that we think about science and so I think from a sort of everyday point of view the thing I would say is it's sort of a different way of understanding the world and you know in from the time of Newton and Galileo and people like that we got concepts like momentum and force and so on and those concepts originally were concepts in physics but we've been able to sort of apply them to our general thinking about a lot of kinds of things in the world we talked about you know the momentum of some product which isn't the physical motion of the product presumably it's it's something more conceptual and and we think about those things in a conceptual way and I think knowing that things are rooted in computation gives us a way to think conceptually about the world with concepts like computational irreducibility principle of computational equivalence undecidability those kinds of thing that I think will have a general applicability to our way of thinking about the world far beyond the specifics of the details of how the physical universe happens to work okay the question was is the universal simulation I think we can fairly say that question really doesn't make any sense and let's see Jonathan and I just worked on you know I this is one of these questions it always takes me a little while to unpeel philosophically and Jonathan and I just worked on a on a nice succinct answer to that let me see if I can find that here it's in the QA section on the website and I think we might have a ok here we go so the okay so I mean actually I guess I wrote this was Jonathan was somehow involved in this um the so I mean the first point is if there is a definite rule for the universe it means everything about the universe is determined from that rule there are no external miracles in the universe there's just this rule that determines how the universe works and so then to say that the universe is a simulation would be to say there is something intentional about this rule there's some somebody some something set up this rule to be the way it is okay so there's a they there's a notion of somebody some programmer program this rule on purpose to be this way okay well we already get into trouble trying to go take intentionality outside the domain of humans maybe even to animals we have trouble but by the time we're dealing with AIS we have a lot of trouble and by the time we're dealing with you know other systems in nature like you know we might say the weather has a mind of its own what's the weather trying to do today is the weather trying to make us wet you know what is it trying to do is there a way of of transport transferring our notion of intentionality to these other kinds of things that's already very hard to do so in this case what we'd be doing is transferring intentionality to the whole universe and saying in a sense was something outside the universe intentionally putting in this rule okay that's first problem second problem that in a sense is an even worse problem is that innocent this rule space relativity idea implies that all possible rules for the universe are in some sense equivalent the rule that is the one that we are identifying in our sort of foliation of the universe is the one that corresponds to our particular way of understanding the universe our particular description language for the universe and so it's some it doesn't really make any sense to say you know they somebody can decide on a rule but any possible rule would work the rule that we kind of consider is the one that is operating is the one that fits into the description language that we can create so it's not something you can really insert from the outside so I think I think we're really we're really pretty pretty unraveled in terms of being able to say the University of simulation I think it really that really isn't a sensible thing to say I think I'll add one weird footnote to that the one thing that in the end one could say about the universe after you cut out all of this all these different possible rules all these different possible description languages the one thing that shines through is the universe is a universal computer a nothing but a universal computer so people have wondered you know is the universe capable you know when we have all the computers that we can construct so far as we know are all ultimately equivalent we can program one computer to behave like any other computer we can make a Turing machine be sort of be able to model any kind of we be able to emulate any kind of computer that we construct whether it's the computer in our CPU chip or whether it's the computer that corresponds to some physical process all of these things can be emulated well we know we can do it for the things that we normally talk of us think of as computations but the question what this model is implying is the one absolutely certain thing we can say about the universe is the universe is just a universal computer and nothing but and for example can you say well what could be more than the universal computer well here's an example a Turing machine for example it might take it might just go along it might go along you say is the Turing machine ever gone to halt ever even after an infinite time well to know that it's a computationally irreducible thing so you might have to go an infinite time to find that out but you can imagine building a sort of super Turing machine a hyper computer that would just immediately be able to answer the question it would just say yeah this Turing machine you've got after an infinite time it will halt or it will never hold even after an infinite time and so a hyper computer is something you can imagine but the question is can we build a hyper computer in our physical universe and this model says no you can't build a hyper computer in our physical universe and in fact this kind of rule space relativity thing implies that even if there was a hyper computer that was sort of that our universe even if even if there were rules for our universe that were possible that corresponding to hyper computing there would be essentially a cosmological event horizon that will prevent us ever communicating with those rules that correspond to hyper computation so there's there really isn't a lot of room for a programmer in this whole story okay let's see um so this question about an approximation to how large the bits and the underlying rule are we have a way of estimating that I I think it's a little bit flaky but the estimate we have is 10 to the minus 93 meters which is really small um let's see okay if we calculate a very fine-grain we should be able to converge to something which seems continuous is that a way of doing continuous computation well the answer is that um what we're saying here sorry I'm a little confused by my on my screen here yeah what we're saying here is that ultimately things are discrete but at 10 to the minus 93 meters that's really really small and so to a very high degree of approximation we are still seeing things which appear continuous like continuous space this doesn't really give us any more of a way to do continuous computation than then I mean we're still doing the computation in the universe so we start to construct the computational elements out of things in the universe this I think might give us some interesting ideas about how we could do sort of massively parallel computation but I think that's a different kind of story um question about why there are four fundamental forces that relates to this question about local gauge invariants the four fundamental forces of the well the standard model is about three of those at particle physics of well okay four fundamental forces gravity the strong nuclear force the weak nuclear force and electromagnetism gravity has always been the odd-odd force out in that sequence we in our models we do explain how gravity works the other three forces we can see how those might arise those forces are all related to quantum mechanics but the real test of those forces are they're known to be associated with local gauge invariants and if we can reproduce local gauge invariants we will reproduce the possibility of those forces but we haven't we haven't done that yet we have an idea of how that might work um okay suppose you had the rule to make useful descriptions of large-scale phenomena would you need to run the simulation because of computational irreducibility ultimately yes to find out that I'm doing this live stream right now from the original from the underlying rule for the universe and the initial condition for the universe we'd have to run that rule for whatever it is 10 to the 500 steps to get to this point and unfortunately computational irreducibility means we'd probably have to really run basically those 10 to the 500 steps and that's something that we don't get to do in our universe our universe just did it but we don't get to do it in our universe now the hope is that there are pockets of computational reducibility that will allow us to make general statements without having to run all of that irreducible computation and one of the big surprises in this project is how thick the layer of computational reducibility is that allows us to derive Einstein's equations to Rive the Schrodinger equation derive the path integral all these kinds of things that don't seem to get in meshed with computational irreducibility they're detailed parameters detailed features of particles may very well get in meshed in those but these general features of physics do not get in meshed in those things and so so we're able to derive them so that's that's kind of the how far the boundary of reducibility is we don't know I mean the realization sort of after the fact is we kind of know they're somewhat thick layer of reducibility because that's why we humans can make any sense of the world if everything in the world was immediately thrust into computational readability we wouldn't be able to make any sort of general statements about how the world works we wouldn't think that there was sort of that the universe worked in a coherent way it would be all thrust into this sort of very low-level computational irreducibility let's see how does the observer effect fit into this theory well I mean a lot of what we're talking about is the interplay between the observer as part of the system and the system itself the fact that when we try to analyze the system we're analyzing it in terms of causal graphs that represent causal relationships between events and we're analyzing it in terms of these foliation zuv the causal graph and so on that's all about trying to effectively model the way that an observer who is embedded within the system interacts with the system you may be meaning by observer effect you may be meaning things like the uncertainty principle I talked about that a little bit earlier about the well again it's all related to the observer as something embedded within the system but that's also related to the geometry of branch field space and some other kinds of things but I'm not not completely sure what what's meant by that hey Jonathan do you have a better thought about that yeah well yeah okay I may be able to add something so when people talk about the observer effect in quantum mechanics as you say they're normally meaning sort of the the effect that the observer can have on the outcomes of certain types with certain classes of quantum measurements and effectively in our model this this comes down to the thing Stephen was talking about earlier about these quaffed these these quantum observation frames where so in the same way as in relativity when you if you have different relativistic observers they can see different orderings of space like separated updating events in the quantum mechanics case where you're in the multi way evolution graph different quantum observers or depending on the identity of the quantum observer you can see different branch like orderings of of measurement events effectively as how that works and again this is probably something we can address in in more detail later oh good answer Thanks um okay let's see does the amount of computation in the universe increase over time as it grows in richness and complexity is it possible to quantify how much that is what does the clock speed of the universe okay so the odds of that is yes the amount of computation that's happening in a sense does increase in time because well at least time as we perceive it because the way that we are foliate in time the way that we are deciding what counts as the next moment of time we're imagining that moments in time sort of go across the whole universe so assuming that we use the sort of the way of measuring time that is the typical way that we think of measuring time then the answer is that the spatial hypergraph is increasing in size as the universe evolves further and we kind of and that's that's or it's yeah it's it's basically certain the spatial hypergraph is increasing in size probably related to the expansion of the universe and that means that in a sense for every new for every new time step in this kind of foliation of time more more pieces more underlying nodes in the hyper graph more underlying relations have to be updated to get to the next thing that we consider the next moment in time so in that sense yes the amount of computation is increasing as we as we go through the evolution of the universe what is the clock speed we actually have an estimate of that let me just look up because I'm forgetting which I shouldn't be doing that Tim let me just see here um see I should I should know all this immediately but I also don't think these estimates and yet that solid um let's see um okay yeah so the the estimate for the elementary time is 10 to the minus 101 seconds so that would be the clock speed of the universe that's the that is the time elapsed between two updating events on a single causal edge between two updating events where we tend to the - 101 seconds and in this estimate and that's the that would be in a sense the clock speed um and this question so there is a an interesting feature in rule space there is also the notion of a maximum a maximum speed in rural space and that maximum speed is related and we don't understand that this that well yet is related to essentially a maximum speed of translation between different description languages so I think what that's going to do is it's going to link algorithmic information theory which talks about the complexity of program sizes with features of physics and I think just like we have the speed of light as one fundamental constant of the universe I think we have another fundamental constant which is the maximum entanglement speed that I'm going Zeta I think there is another fundamental constant of nature which is the maximum speed and rule space which we're calling Rho and that maximum speed and rule space is essentially the maximum rate at which translations between description languages can occur and that as I say is is somehow related to a gives a scale for program size which is so just as the speed of light translates from elementary time to length the maximum entanglement speed translates from elementary time to essentially quantum units essentially h-bar it translates to sort of quantum extents in branching space so the there is a translation from elementary time to distance in rule space and that distance in rule space is somehow related to program length and so there's a there's a way I think of connecting program length which has always been this this rather abstract thing to something sort of physical don't yet fully understand that but I think it's a coming attraction so to speak ok next question from Peter here does the you know does the theory predict how the universe ends no we don't know that we strongly suspect if that the universe will go on forever that it corresponds to a computation that will not hold there's a whole bunch of reasons to believe that in this kind of model but we can't um we can't say that for certain I mean the there is the possibility that this computation will eventually reach a final state where it just says and the answer is 42 or whatever but it seems very unlikely that would it's very hard to make that consistent with causal and variance it's hard to make that consistent with things we already know it true about the universe but it is not absolutely ruled out by this kind of model um okay if experiment produced a Turing Oracle or a hyper computer would that disprove the theory yes that would disprove this theory um however good luck on connecting such a hyper computer - anything that our senses can deal with because what we in everything we've done in science we have tried to reduce what we observe in science to essentially symbolic representation and a symbolic representation is a finite symbolic representation and it is incapable of representing the kinds of raw material that you need to actually interact with a hyper computer so even if we had a hyper computer sitting under our noses we wouldn't know it because we just don't have a good way to interact with a hyper computer because of the fact that our way of describing things and even probably thinking about things is rooted in kind of this symbolic notion of doing things um somebody's asking can we get a copy of the projects book signed by Jonathan Max and me not sure we we've been we were considering as we thought about this project and we tried to understand what things we could provide for people in this project and how people could be involved we we I have to say that swag was up there in the in the list and and kind of the adopt the universe kind of idea from the registry is also something that some that's on the list and so we're hoping to to be able to provide some of those things but mostly we're we're just really keen I mean we see this as being a a sort of a big intellectual adventure it's kind of like can we climb the tallest possible Mount Everest of science and you know we don't know if we'll get to the top and we don't know whether it's you know it'll take a century to get to the top but we think it'll be it'll be fun to see what happens on the climb and we hope other people will help in that climb but we hope also that people will find it interesting to see what's involved in in getting there and to see what um you know in in in our efforts to kind of be do sort of frontline science what's actually involved in doing that um let's see so a question here do the updates the hypergraph happen in parallel what happens in the case of collisions yeah that's the whole point the the the there are many possible up datings that can occur and the fact that there are those possible up datings defines this multi way system which is the source of quantum mechanics and the what does it mean that they operate in parallel well there's a set of causal relationships where one thing has to have occurred before another can occur that defines the causal graph it defines a partial ordering of those kinds of update events and that's that's it's the whole story of what possible sort of total orderings are consistent with that partial ordering which translates into what what do we consider this sort of the the successive steps of time in our universe that's kind of what how the whole thing sort of sort of works out and it's this invariance of the ordering of what happens when things occur in parallel that corresponds to call invariants that implies special relativity that implies sort of objectivity in quantum mechanics etc so yeah it's a very critical thing that these things can happen in parallel and that the that the quotes collisions those collisions are are precisely the that the sort of those lead to the entanglement so to speak that happen in quantum mechanics and so on can the the nominal average guy contribute to this project you know we're going to have a distributed computing mechanism where you can run some some little fragment of searching for the universe on your computer that's one nice way to to contribute I would say that that we don't know what kinds of thinking are going to be needed to figure out everything that needs to be figured out here and there's a there's a lot of kind of both both I mean some aspects of this are going to be at the front lines of sort of quantum field theory general activity those kinds of things they kind of need sort of a phd's worth of physics knowledge to really be be be fully engaged in them but there's a lot that's happening in sort of the computational level where you know we're operating really from the ground up we don't know anything yet I would say that a lot of the work that I did in a new kind of science and so on exploring different kinds of systems there's a lot to do there and there's a lot of intuition to build you know I mentioned using string substitution systems as a way to get an understanding of the multi way graph and so on there's a lot more that can be done along those lines and and this is a very young field so there's a lot that can be done by you know without having a physics PhD there's a lot that can be done by just doing computational experiments trying to make conclusions from these computational experiments trying to devise kind of general principles on the basis of those experiments and I don't think anybody has a great advantage in doing that I mean I've I've been doing that kind of thing for 40 years now so I kind of have developed a certain amount of intuition about it and and can do these things a certain speed but in particular the you know the tools that we have in Wolfram language part of the reason I built Wolfram language was to have what I needed to be able to do those explorations so those tools are very well optimized for those kinds of explorations and as I mentioned the the dwarfing language functions and things for doing evolution according to these hypergraph models and so on are all as of today available through our function repository and you can get them through through the website and so on and so you can you can explore these things and you know it's real open-field nobody's explored these things you know we we've just started we've just been picking away at the edge of it so I think exploring kind of both these full hypergraph rewrite systems those are just a bit complicated but exploring these analogs and string rewriting even in things like cellular automata highly useful and it's just like this it's a really wide open field where there's just a huge amount to do and I think my only um you know one of the things that's happened from my work on new kind of science is you know we kind of I really pushed this idea that one can make models for for things in the world for just things in nature things in social science whatever on the basis of programs rather than mathematical equations and it's really a pretty neat thing that's happened in the past 20 15 years and I'm not I'm not saying that it's all my fault so to speak but I think the new kind of science book kind of was you know I was that was really the the the the idea that that I really pushed in that book was this idea use programs to make models of things rather than using mathematical equations and after you know it's basically been a 300 year run of people primarily using mathematical equations to make models of things last 15 years there's been a pretty thorough transition to using programs to make models of things and that's pretty neat thing to see it's something that's kind of to me it's a little ironic because a bunch of people when my my book came out said couldn't possibly work never gonna be useful programs never useful for anything and now that's basically what everybody does so that's kind of nice but the one area where that really hadn't made progress is in fundamental physics where the idea of using programs to make models of things hadn't made progress is in is in studying fundamental physics and I think now we kind of cracked that nut of seeing how one can use programs and computational ideas to model fundamental physics so that that's that's something that I'm sort of excited about here but I think as I say the the sort of the best contributions to be made you know if you really want to get into the intellectual meat of this is study simple programs study what they do either the real full hypergraph or these simplified cases and try and build up principles about what happens and try and find phenomena you know you might find some weird kind of new singularity that corresponds to some bizarre sort of mixed quantum mechanical [Music] relativistic black hole or something you could find that by just studying these hyper graphs and the evolution of these hyper graphs the trick in these things as always you see some weird phenomenon on the screen the thing that's just maddeningly difficult is understanding what does that really mean but there's a lot that can be done by just saying in the simple cases just look at these cases make a systematic study describe what you see systematically and that's part of the building block that can make science and that's what a lot of science is just good science is about doing things systematically being able to have a good presentation of what you find and so on I mean I would say that in this project the thing that sort of happened over the sort of 40 years or so that I've been sort of picking away at things somewhat related to this the it's been sort of a gradual understanding of more and more of what the significance of things is and a gradual realization that you know often it's that thing that I sort of understood I sort of had seen but I didn't really understand its significance and then I progressively understand more and more of its significance and that's typically the slow part at least in my experience all right we should um take a few more questions and then probably wrap this up for today um let's see what amount of simulation is required before enough information can be found to compare the rule to existing theories we don't fully know the answer that I said there's several times here I mean we we just don't know um we we don't know um about the universe's in the registry of notable universe I think we haven't finished actually we were rerunning the registry just last night and I think they didn't finish running so I think we've got about a thousand universes those are really just universes that came out of various searches they were based on various criteria they seem to have some interest or another they're really pretty arbitrary I mean that's a that's a just the universe that just does nothing or makes this very simple tree those don't make it for the registry these universe is that for one reason or another it's like oh that's kind of interesting put them in the registry we're sort of over generating things for the registry in the hopes that we'll capture things that will be useful examples to study and in talking about you know what does the the average person do in this project you know what we haven't even looked at every page in that registry we don't know what's on there we don't know what there may be a bunch of really weird and interesting phenomena there that we haven't even seen yet so that would be a good place to start um let's see does the theory whether a hot dog is a sandwich you know one of the things the theory says is there's a lot about the way we perceive things that is in the matter of how we perceive them and so I don't think we have anything directly to say about that other than that there are different description languages for the world and that they're sort of equivalents between these different description languages and it doesn't answer your question um the this is somebody commenting that they like what Jonathan had to say I do too Jonathan is has been a great contributor as Max has also to this project and I hope tomorrow Jonathan will be a big part of the more technical explanations that we're giving um it's question here can we explain the principle of least action in the context of hypergraphs the answer is basically yes we can reproduce the path integral of quantum mechanics from which you can derive the mechanical principle of least action and the way that works as I was mentioning is it's kind of the analog of things sort of an analogue of Einstein's equations in brass real space rather than in physical space and that's what Tim that's that's what can that that's what leads to this okay there's a quest using the Turner and completeness of the rules to do massive computations using tiny structures in the network that's kind of how the universe is is building itself for us I think all the time is it's doing a I mean one of the things that really took me a while to come to terms with is this universe is such a waster of computation I mean there's just unbelievable amounts of computation happening to just maintain a little tiny piece of space and that's that's something very weird now can we harness that computation for something that we think is useful I think it's useful to maintain space but can we can we harness the computation you know in a way that's sort of purposeful to us we don't know how to do that yet that's obviously a very interesting thing to think about the length scales that are involved here are really really tiny so that's a challenge but there may be ways to do it um okay low entropy at the Big Bang yeah I think I talked about that a little bit what what what I think is happening is that the initial conditions may be very simple but essentially what's happening is that the evolution the irreducible computation that's happening in the evolution of the system is so encrypting those initial conditions that for us as sort of computationally limited observers we can't decrypt that and when we can't decrypt it it looks random to us so it looks like it has high entropy and that's it's it's that phenomenon that leads to the this the the second law of thermodynamics and the apparent increase of entropy and the low entropy of the inertia which which means that we can start from this low entropy this very simple initial condition and wind up with this higher entropy with with with the law of entropy increase and so on um to get comments from established physicists orally oh yes lots it's been kind of interesting I we haven't had partly because of the pandemic we haven't been sort of communicated as much really might it had only one sort of fully interactive session with a group of friends of mine who were sort of established physicists I was a lot of fun as I would say they were getting it which is really good and they were like this is really neat so that's that's good I'd been just in the last 24 or 48 hours we've been sending out sort of preliminary versions of some of this stuff and I'm sure while I've been on this livestream I've had a whole bunch of other responses and you know it's what's interesting here is the methodology the underlying methodology is a bit alien but as soon as we've gotten up to the level of sort of connecting to things like quantum field theory and general relativity it's actually quite familiar and as I mentioned one of the really nice things is this correspondence to a lot of kind of theories that have emerged particularly in the last decade or so in physics particularly as coming out of this 80s CFT respondents and so on and I think that really helps in making this connection to sort of the the you know I used to be an established physicist so I the established physicists is probably the wrong wrong description I I think I'm I'm I'm part of that group although I've been kind of out of the business for a long time now but you know what's happened it's kind of a funny sort of time walk for me because you know a lot of the people who've been sort of leading physicists were you know friends colleagues of mine back when I was doing physics I happen to be a bit younger than most of them because I started doing physics when I was pretty young and so it's been really strange for me because I've been following physics all these years but I haven't been really deeply involved in it it's kind of interesting for me to go back and look okay what happened to this particular thing one of the things that has happened actually in physics is that there were many different strands of development that existed and one of the things that has happened in sort of the the established physics kind of thing there's a lot of those strands have merged in different ways so things that would be in completely different papers will now find themselves as words in the same sentence and actually that unification I think we can take that a lot further with this with this theory and but the fact that we've kind of relating to a lot of those things I think is is very helpful in making a connection to physics you know one of the things that so I'm I'm I'm really hopeful that we'll be able to to leverage what people have already studied a lot of the sort of technical work in string theory Twista theory all these kinds of things will be oh okay that means we can say this in this and this in addition to what we've been able to say and one of things we hope to do on our live streams is have discussions with some of the leaders in those various fields many of whom I think I would consider to be friends of mine from back in the day when I used to do physics and be able to talk about how their theories and the mathematical developments of their theories particularly relates to what we're doing here how does this defining a context-free grammar for physics well okay so these hypergraph rewriting rules are like graph rewriting rules typically context-free grammars operate on strings just sequences of things these are like graph grammars the the theory of graph grammars is not particularly well developed but you can think about these things as being kind of like hyper graph grammars except that our objective is a little different from a typical grammar and typical grammar what you're trying to do is say parse this English sentence for example or parse this piece of a programming language code or something and you're saying you know break it down make a tree out of it and you're doing that by by saying there are these rules and I'm going to reduce the thin thing down to the tree that could be used to generate it what we're doing instead is sort of running that process in Reverse and we're saying take this starting point and sort of do all the possible Treeing out of what could happen and in some sense what we're doing is like running a graph grammar kind of in Reverse running a hypergraph grammar kind of in Reverse and that's sort of what what is really going on here and we are we are the intermediate our whole existence and the whole universe is the intermediate stages the non-terminal nodes effectively in the running of that hypergraph grammar in Reverse is it possible to write unit tests that would validate the presence of certain physics analogous features when a particular rule is run hmm so gosh how to think that you know one of the okay let me try and take that in the following way so one of the things about existing science particularly experimental science is the idea of doing isolated experiments so in experimental science the typical thing you try to do is to say I'm gonna do an experiment on this piece of this system and nothing else matters I'm going to be able to try and isolate the effects in this particular area of the universe to just do an experiment on this um now that's something that has been really critical in doing experimental science one of the features of these models is that everything is really connected together so it's actually more difficult to be able to you know as we've been working on studying these models one of things we've often done is say let's idealize everything away let's just make a swatch old black hole and nothing else well it turns out you can't do that you have to have all the other stuff that goes around it you can't just make this isolated black hole thing without any of the rest of the the universe sort of hanging around it and our least we have we don't think we can do that um so you know we spent a bunch of time trying to do these idealized experiments based on sort of separating out isolating out particular effects in the universe and and being able to study those separately and that turned out to be pretty hard in other words sort of everything comes together in this model of the universe so teasing out being able to look at these limiting cases where you can sort of do a unit test and just test that particular feature without testing other features is quite difficult and that's one of the challenges in sort of finding those ways in which you can use sort of computational reduce ability to tease out those unit tests I might say that I it's a little bit of humor here that Max is is a big enthusiastic unit tests Max is probably the most the most software engineering of our little team here and one of the things that I've continually given him a hard time about is that he insists in building with the fundamental code that we've got that runs these models in setting up unit tests for every possible aspect and doing continuous integration of all of this code and I've been sort of complaining that um you know we're we don't even know where the certain aspects of this model are right and so you know you shouldn't be doing all these precise unit tests but I'm really glad he's done those because it means that we know the code is really doing what we think the code is doing but I'm just kind of amused that the unit tests of the question of doing unit tests on the universe is sort of reminiscent of doing unit tests on the models of the universe which we've been max has been a big contributor in in doing in this project okay so a question is are there general methods to discover where computational reducibility is that's a really interesting question I do not know the answer you know machine learning kind of might accelerate what is essentially our human poking at things and I we've used machine learning I've used machine learning a bits in analyzing some of these models and so on but I don't have a really good answer to that I think that say the sort of that is that is like the automated scientist so to speak looking for computational reducibility is looking you know the reducibility is the place where you can make a scientific law so asking to sort of automate computational reducibility finding is like looking to automate the doing of science so to speak and with a little bit of the ways towards that but we don't know a really systematic way to do that all right well I think we should wrap up here so well thank you all for coming this is I'm really excited to to launch this project I hope people will choose to get involved I encourage you to check out all the things on the website start playing with the actual tools that we've provided give us feedback I bet they're a bunch of professional physicists on this livestream and mathematicians so there's really I hope things things to dig into there as I say tomorrow we plan to do two more Q&A s14 primarily more professional physicists and mathematicians where we'll really get into the into arbitrary levels of detail other people might find it fun but I don't guarantee that we'll explain everything we're talking about there then following that QA will be a QA about kind of the philosophy of this some of what it means to find fundamental theory of physics in this kind of way then we are planning to follow up on Thursday with a QA about computer science where we'll talk about the kinds both sort of this from a computer science point of view and possible implications of this for for thinking about fundamentals of theory of computation and so on well thank you all very much and we'll hope to see you all on another livestream another day thanks you

Channel: Wolfram

Views: 292,981

Rating: 4.8922744 out of 5

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: rbfFt2uNEyQ

Length: 229min 40sec (13780 seconds)

Published: Tue Apr 14 2020