Wolfram Physics Project: Math & Physics Technical Q&A

let's go ahead and go thank you okay hi everyone so we are going to do a Q&A about more technical physics and mathematics issues related to our fundamental theory of physics project and it'll be primarily me and Jonathan gorod who'll be trying to answer all those difficult technical questions I might say that at 4:00 p.m. Eastern time we will be doing another Q&A about philosophical kinds of questions where we'll cover more general interest sorts of things what we'll be doing here we'll probably may get quite technical and we'll Mike some effort to try and explain what we're talking about but it might get some it may be one of those look it up on the web if you don't know what the word means type type stories okay let's get going so let's see do we have a first question um okay so a question from Kevin on Twitter does this model resolve the Bell paradox I don't see how causal mechanisms can handle quantum interference between branches okay I might also comment that we've written some q and a's that address some of these questions so Bell's Theorem in quantum mechanics I think Jonathan wrote that QA so maybe I'll pass this to him for an answer to that question yeah sure so um I'm hoping you guys can see me with with trying to debug the video sets up let me know if you can't so the way that you get resolution of the way that you can prove compatibility between our models and Bell's Theorem is the proof works in largely the same way as it does in other kind of deterministic non-local theories of quantum mechanics like the deployed bomb sort of interpretation the the pilot wave interpretation so the essential idea is we generalize the notion of causal from merely kind of causality in terms of space like locality which is normally how you think about it in the context of relativity to this notion of causality in in terms of branch like locality or a branch flight causality so if you've read sort of Stevens announcement post or his or his technical introduction you'll be familiar with this concept of what we call the multi way causal graph so this is a generalization of a spacetime causal graph where it has a causal connections not only between different sort of updating events on the same branch of multi-way evolution but also causal connections between updating events on distinct branches of multi-way evolution and so then so the idea is therefore you can have events causally influencing influencing each other not only because they're close together in space but also because they're they're close together in a branch you'll space in this more abstract structure which we which we have various kind of conjectures about the limiting case of a branch chill space becoming effectively a projective Hilbert space as you'd expect an in standard quantum mechanics and so it turns out that gives you a fact of a espeacially non-local correlation between in your hypergraphs that's sufficient to prove a violation of the CH SH inequality and therefore to sort of prove consistency with Bell's Theorem one thing about quantum interference just while I remember so so again there's there's a Q&A answer I wrote it on the website about this but the basic way that that works is okay in the context of say a double slit experiment um what you can have is a multi-way system where effectively on one multi-way evolution branch the photon goes through one slips one multi-way evolution branch with the photon goes through the other slips then when you apply this completion procedure that this process of performing a quantum measurement where effectively you define equivalences between states all those multi-way branches the when you define those equivalences they those allow for new states and the multi-way evolution graph to be reached and in the case of something like a double slit experiment those correspond exactly to the interference States where the photon essentially went through both slits and interfered with itself that's that's a kind of a very tough summary of how interference books within our model I know we can go into more detail if you guys are interested hey Jonathan is there a place in your quantum mechanics paper where you discuss this more formally yes yeah there is hey let me actually plop a section reference if I can in just well why don't you pull up the yep right to do that I'll slip up no I can I can share screen hang on okay hopefully that's now visible okay so the proof of compatibility with Bell's Theorem this is well hang out we can do a search for CH SH so the the yeah okay the proof compatibility with Bell's Theorem is in this section three point for Bell's Theorem particles and consequences of multivariate relativity and basic notions of interference are actually introduced much earlier than this when we when we first discuss this notion of the multi way evolution graph and and so this completion procedure the observers performed so basically the whole of section 3 can at some level be filters introducing formally this idea of interference between between distinct and healthy way branches so yeah if you want to know more about this specifically definitely check out section 3 of my cosmic annex paper ok all right let's go on to the next um next thing here okay Adam on Twitter says um mentioned possible physical experiments towards the beginning it's unclear what is testable from the model giving computational ready stability what finding would strengthen or weaken this framework okay well let me take that a little bit so so the issue is computational irreducibility implies that if we want to know the detailed outcome of the specific evolution of the rule that's irreducibly difficult to find one of the big surprises in this whole project is the thick layer of reducibility that sort of sits on top of sort of the the structural flexibility of this model so in other words and and in fact in retrospect I think this is to be expected because it's that computational reusability that allows us as sort of human observers to have a chance of making sense of the world if everything we saw happen in the world involves computational irreducibility to understand we would have a hard time kind of making sort of general statements about the world so I think the in terms of physical consequences I think we should distinguish probably two maybe three kinds one is well something like relativity or sort of our quantum analogues of relativity these are generic results these don't depend on details of the rule these these things about the interplay between quantum mechanics and relativity these are all generic and so there are likely to be statements about for example some of the dynamics of black holes and so on that can follow in a way that doesn't depend on the underlying rule I think we also think it's likely that there are statements about quantum computing maybe some statements about repeated quantum measurements that might be amenable to experimental observation in the short term that again might be quite generic then there's a whole class of things that there's a course of things that probably extremely specific to the particular underlying rule may be particle masses I'm not sure as I say I think an intermediate case is gauge groups where I'm sort of hoping that there will be some results that can be gotten that will be a little bit more generic just as I I would expect that there's a large class of rules that will give integer dimensional space as a limit I suspect there's a large class of rules that will give a lis group as the local gauge group as a limit now maybe we can talk a little bit about some quantum quantum experiments and the possibility of directly accessible kind of or I should say another thing for example this idea about elegans these these ultralight particles this is something which sort of interesting in terms of its prediction status because it's it's not something where we can nail it and say okay given this rule there's this particular thing it's just there is sort of an easy possibility to see why there will be much lighter particles they might not exist it might be that the first sort of solution I mean we can think of these particles as being like solutions to some kind of generalized equation that represents the possibility of locality in in in these some so timing to be a little bit more formal you know I've always viewed for example in cellular automata the existence of localized structures as being like solving some sort of generalized by Fantan equation with respect to the evolution operator that represents the cellular automaton and we can see expect the same kind of thing that these localized particles are some kind of sort of eigen solution to some kind of evolution operator in there in the hyper graph and it is certainly conceivable that the first solution could be of size 10 to 35 but it seems more likely that there are solutions much smaller than that and that's a statement that we couldn't prove that mathematically but if we just are used to looking at die fountain equations it's a rare die fantail equation whose smallest solution is the water at 10 to the 35 so that's kind of where that where that sort of intuition comes from and that's it that's a funny kind of prediction because we're not saying we know the particular number nor are we saying it's a generic prediction that is something to do like the the validity of equations or something like this but maybe we can talk Jonathan maybe we can chat a little bit about some possible nearer term quantum measurements and predictions and so on sure so okay so yeah so one example of a prediction that seems to be relatively generic at least if our sort of current model of how quantum mechanics works in these models is correct is a bunch of results with regards to quantum information theory and kind of quantum computational complexity theory that Stephen sort of alluded to so so one example of a result is okay so so some of you will know kind of our our one way of modeling quantum quantum measurement within our models is you take this multi-way evolution graph and you apply these you make equivalences between different branches so that effectively that the effective multi-way evolution collapses down to how to have a single thread of time and this is in some sense equivalent to this process of kind of walling off certain quantum states by constructing a sort of curved measurement frame that Stephen mentioned earlier in the in the live stream yesterday so this procedure if it's correct if this is a correct model of quantum measurement make certain predictions about computational complexity so here's an example of a definite one the structure of the multi way evolution graph gives you actually I think in my opinion a really really clean intuition for the distinction between maturing a standard classical Turing machine a non-deterministic Turing machine and a quantum Turing machine because if you think of every multiwave branches corresponding to a sort of as performing a computation then a classical deterministic Turing machine is effectively following one single multi-way branch in accordance with it with a completely predictable deterministic rule a non-deterministic Turing machine is effectively following multi-way branches again it's following a single multi branch but where the path this Scylla is selected by some non-deterministic rule finally a quantum Turing machine is the whole multi way evolution graph itself right it's evolving a linear superposition of different eigenstates which you can think of as being the different sort of microstates on each on each branch of the of the multi way evolution graph but the point is you know in standard in the way people usually think about quantum computing one of the hard things about it is and the reason why it's not quite correct to just think of quantum computers as being like kind of exponentially parallelized versions of classical computers is because you have to set up the initial conditions of the computation really really carefully so that all the different eigenstates where you've got basically the wrong answer have amplitude so they all exactly cancel out and by the end you're just left with one eigenstate that gives you the right answer and that's why quantum computers are so hard to program conceptually we have exactly the same problem here right see if you what you have to have it you have your multi way of relation graph but you still have to perform a measurement on it to collapse it down to a single evolution history so that you get a single classical result as the outcome of your computation well when you do that there's a fancy mathematical way of thinking about this which is called the kinetics completion procedure and basically and so at a mathematical level what happens is the transition monoids that is the analog of a transition function for a quantum Turing machine if you apply the kinetics completion procedure to this finitely presents a transition monoid it reduces it to a finite transition function and the space of quantum states of the of the Turing machine collapses down to a classical during a state of space of states for an ordinary Turing machine and this implicate that this has immediate implications for effectively the extent to which the complexity classes of P and B QP that is sort of classical polynomial time and bounded error quantum polynomial time can be related and as far as I'm aware it's it's sort of this is one of the the most concrete predictions that we're able to make is that we actually have bounds on the extent to which P and P 2p can actually be related and that's potentially one way of verifying and or falsifying so at least our model of quantum mechanics it's not the whole underlying model but you know one of the things there is that the the my concern an issue with that is that in the end the you know the parameters that enter the bqp you know P comparison will end up being things about maximum entanglement speeds and those maximum tangle mid steeds a appear to be very very far away from what your average physicist with a you know cryostat can can achieve do you have a comments on that yet yes I mean this is kind of the problem so yeah you're absolutely right I mean the this experiment is in principle possible to do but because that you know the maximum entanglement speed is kind of phenomenally huge it's entirely conceivable that the kinds of computations you would need to in order to be able to effectively distinguish p and b QP within a within a real quantum computer are sort of so extremes that they are completely out of the house of current experimental range without knowing more about the particular details of the rule and without having better sort of dimensional analysis of you know estimating quantum entanglement rates and how they relate to quantum computing rates which we haven't really done we have some ideas about but we haven't really done that in detail yet until we have that it's it's kind of hard to say but it's at least it it's one it's one avenue of experimental verification that it is at least in principle possible so for another live stream we'll talk about quantum computing in its relationship to all of this this will be fun alright let's keep going here we've got gosh we've got a lot of questions here okay um Cyril on Facebook distances have to be large compared to individual hypergraph connections but small compared to the whole size of the hydrograph if distances grow larger do you see deviations from one over I guess that's r-squared rules as currently observed for galaxies rotations and modelled by dark matter and tropics gravity in the style of Monde type theories so okay interesting question so the question there is is the inverse square law of gravity going to be violated by things happening so of course you have to realize you know the gravity in you know in in in standard relativity and standard general activity one's not it's not inverse square all the way down the line so to speak you know that that's a but I think a question a question for us is so for example having the Schwarzschild solution which does have 1 over R squared gravity you know having the Schwarzschild solution be you know reproduced in our in our setup I think that's that's an EC I mean what to say about this um okay the current I had originally thought maybe this deviation from three-dimensional space would be something that would be readily visible in sort of cosmology or astrophysics today and that's still conceivable in fact my other thought is that there may be a way to reformulate general activity in terms of sort of tiny dimension change rather than curvature change we don't know that yet that's an interesting mathematical direction we just don't know yet I think the the question of well let's see you know I mean my current thinking is that on the dark matter question that these kind of very light particles are a more immediately plausible thing to look at when it comes to that rather than I mean I've always been my my suspicion that the whole dark matter story would turn out to be a problem with general relativity but I'm getting less convinced about that and more convinced that there might just be some sort of particle oriented solution but Jonathan do you have a comment I I do not know about entropic gravity so do you know about that I know a little bit I know a bit more about mom when was her mother's this woman this modified Newtonian gravity idea or modified Newtonian dynamics this idea that there could be yeah that there could be macroscopic deviations from one over R square that sort of at the level of super clusters and things so actually the way that we've derived general activity or the release the way that we currently understand general relativity within our models does then imply that there could be something there could be some higher order correction to the Einstein field equations it would be not unlike the Mond approach so Stevens already mentioned that possibly one of the most fruitful avenues for kind of investigating this dark matter problem is through these all agon particles but there is at least another possibility that I think is also definitely worthy of further investigation which are these higher order Corrections so um in okay hey let me slow that because that that's a good point but let's get it I can I can give it a little try I mean I think you know that for example long ago I worked on deriving fluid mechanics from underlying molecular dynamics of simple cellular automaton like particles and what you find when you do that is there's leading terms that have to do with continuity of fluids the next order term has to do with viscosity of fluids and there are higher order terms that represent other kinds of detailed features of fluids that are often more sensitive to the details of what particular molecules exist in your fluid now the Einstein equations as we've derived them you know make use of only that sort of first-order non-trivial term and I think Jonathan I don't know whether you ever did this in did you do this in your paper did you get a higher order term in your paper or not yes yeah or at least I got I got a plausible formed one yeah the okay and what does it look like you want you want to show it yeah yeah so I can so it actually it has the basically the same form as this higher order correction that exists in this thing called Lovelock gravity it was actually just before I show the paper let me let me add one thinks that Stephens fluid dynamics point so it turns out this this analogy is far deeper than than either I think well certainly than I expected and possibly far deeper than Stephen expected as well this this notion of when you you know when you go from discrete hypergraph dynamics to derive you know continuous general activity it's like going from discrete molecular dynamics to it's a continuum fluid mechanics it turns out exactly basically at a mathematical level exactly the same thing happens and you get the higher order Corrections in exactly the same way so it in fluid mechanics what you do if you want to if you want to recover the euler equations what you basically you take the the stress and the total stress tensor that exists in the navier-stokes equations and you decompose it into a trace part and a trace free part and then so then the the trace free part is your shear stress and that you kind of assume you just you don't care about that's the high-roller correction and then the trace part manifests as hydrostatic pressure which then appears in the Euler equations but then when you want to compute higher order Corrections to your equations you then have to add back in the contributions from that from the trace free part from that from the shear stress turns out exactly the same thing happens in our derivation of general relativity so what you do is you take this complete discrete Riemann curvature tensor that we derive which is this you know this is higher order tensor and then you decompose it into a trace pass on a trace three part and then so that rate the trace part is then the the Ricci coverage tense that appears in the Einstein equations and the trace free part is this vile curvature that kind of a bit incorporates the information not just about the volumes of the geodesic bundles but about the shapes of the geodesic bundles as well so the ordinary Einstein field equations only put constraints on the Ricci curvature they do they leave the viol curvature completely unconstrained but our derivation at least leaves open the possibility of their existing these higher order Corrections that also put constraints on the viol curvature and one possibility we haven't looked at in detail is that these effectively correspond to deviations from from large-scale Newtonian dynamics we might have we might be able to see cosmological consequences that let me see if I can quickly one piece of intuition that's quite useful I think is is that what the Einstein equations say if you have a bundle of gd6 the you know the overall area of the gd6 the geodesic bundle is given by the Ricci scalar but the you know when you look at the shape of the JDC bundle and how the shape of the geodesic bundle varies that probes higher-order pieces of kind of the curvature the curvature tensors and so on and so the you know the the traditional statement of the Einstein equations is saying that essentially the area of this JDC bundle is is not changing but there if you have sort of higher-order pieces that's talking about different kinds of deformations that are not possible in the judie tzuke bundle okay let's see let's see Jonathan's papers let's see let's see the tensor okay sure okay so this is the standard there of the unspent equations but then we note that this derivation is basically okay so in in fluid mechanics you have this Boltzmann equation you're basically you're starting from the Boltzmann equation for the you're starting from the one particle distribution function for the and it's Boltzmann equation and from that you're performing this thing called the Chapman and Skog hydro dynamic expansion which is basically just a kind of it's the tensor analog of a power series you're basically expanding and some in some small parameter epsilon and then use this to drive the continuum navier-stokes equations and basically what I show is that if you do exactly the same thing but now this instead of the the one particle distribution function you you use this this function that I call C which is effectively the this is the the the volume of a of a cone of a space-time cone in the caused little graph and you treat this as like the kind of hypergraph distribution function then you end up deriving the Einstein equations and effectively the same way but you also get but in addition so this this piece here contains the standard Einstein equations but there are also these higher order Corrections that turn out to have the same form as this thing called the Lovelock theory of gravity at least in it in some approximation so these are these corresponds to higher order contractions of the Riemann curvature that place additional constraints on this quantity here which is the viol curvature and this has potentially makes predictions about things like gravitational waves and about and about how kind of galaxies interconnector acts gravitationally on very large scales but we don't as I say we don't yet have sort of quantitative results for it for example what is the dimensional analysis of alpha beta and gamma do we know the order of magnitude of those correction terms this is a so on for we know that alpha and beta are very very small that's that's about a bit are they dimensionally different from gamma there that I would need to check I uh okay anyway all right yeah I can look into that I don't know how much the okay so interesting question all right um let's see let's keep going here olav on twitter um relation on screech model does special and general relativity appear naturally with some rule sets yeah the answer to that we talked about at some length whenever there is this phenomenon of causal invariants and then you get special relativity when you in addition require that space be finite dimensional then you get general relativity and that there are probably some sort of detailed mathematical footnotes that might be appropriate to put in there about the way that limits work I think that Tim as we think about deriving things like general activity it's a stack of many kinds of limits the the we're dealing with length scales large compared to the elementary lengths the distance between nodes and the hypergraph we're dealing with timescales large compared to the elementary time we're dealing with but yet these things have to be small compared to the overall size of the hyper graph and so on there's a stack of limits that there's certainly more mathematics to be done in really nailing down exactly what what kinds of sequence of limits and interchange of orders of limits and so on have to have to be made but yes with with with those with with some as yet unknown sort of perhaps pedantic or perhaps important mathematical footnotes it follows as soon as you have a model with the structure of hours and you have causal variants and you have this requirement of finiteness of dimension of space and you have this additional requirement of essentially computational irreducibility which is I think one of the one of the easiest to achieve requirements then generativity follows with these even potential higher-order terms that Jonathan was just mentioning um get specific that predict gravity galaxy rotation nan arbitrarily no I mean to work out the rotation of a galaxy you're basically solving some n-body problem with with some gravitational force law and the the thing that Jonathan was just mentioning is maybe there is some correction to the gravitational force law that will be implied by these higher-order terms and the Einstein equations remember remember the the the big story here is we can derive the Einstein equations normally the Einstein equations is just a thing you put into a theory so there's no possibility of saying we can derive them and we can derive I wrote of corrections it's just these are the equations now go solve them as in fluid mechanics you know the analog and fluid mechanics to the Einstein equations that there's navier-stokes equations but they're navier-stokes equations are something that you expect to be deriving from small scale molecular dynamics so for example when in an extreme case in hydrodynamics when you are close to the speed of sound and you start forming shocks and a fluid it is no longer the case that the navier-stokes equations which assume a purely continuum fluid and ignore the possibly the presence of molecules they don't apply anymore and so you have to make corrections to those equations and I must say that I had long thought that when one had extreme gravitational situations close to singularities and curvature and things like that that one would similarly see that that it would turn out that the Einstein equations were just an approximation in the same way that the navier-stokes equations are just an approximation to the true dynamic server of a fluid made of made of molecules and I guess that that one of the exciting things here is that we have the serious possibility of deriving those higher order Corrections to the Einstein equations on the basis of the underlying discrete model okay let's see F speech on Hacker News could I understand the effort this way in general any Turing complete set of computational rules should be able to generate any computable expression and hopefully physics can be expressed with computable expressions at least if it is to be comprehensible to humans looking for a particular set of rules and study the English language and math symbols that meet some kinds of aesthetics do you expect only valid physics to be expressed or is the research on a kind of restriction that will lead to only valid physics being expressed okay that that might be better in our philosophy Q&A later but but let me try and say something about that the in the first sort of explanation of what we're trying to do it's find a rule where we can go work out its consequences and match them up with no in existing physics now if you peel that back a bit it gets a little bit more complicated because what does it mean to match them up with existing physics it could be there's a different description for the universe that isn't doesn't happen to follow existing physics but is also a valid description of the universe and that's what when we talk about this kind of rule space relativity that's what we're talking about is looking finding a different description language which is also a valid description language for the universe that we can then match up with and in the end the one sort of untrained ring constraint is that these description languages correspond to a universe that is in a sense just a turing-complete universe but so so the the I would say that the main thing that should be considered the the core of the project right now is we built up physics over the last 300 years or so roughly I mean that's the main main development of physics as it exists today kind of started with Galileo and Newton and so on and that means we've got a summary that works for us humans although it's pretty difficult to work with it's really non-trivial to work out consequences of general it's a video consequence of quantum field theory but it's something where we've got the sort of a human path to working out things about the universe we've summarized the universe in terms of existing physics what we want to do is to find essentially a rule that reproduces that existing summary of existing physics whether there is a completely different way to describe the universe that will be appropriate if we had completely different senses if we were if we were dealing with completely different kinds of things is sort of more of a philosophical issue but then we would want to describe that with a different rule yes that is likely to be the case and that's what this rule space relativity is about and I have to say we're only slowly I mean that was a very new realization that that rule space relativity idea was was out there and we're just I think starting to grapple with with what the real consequences of that are all right let's see um okay question from Jeffrey Sims why stop hypergraphs at two edges is there a series of an edge hypergraphs to be considered okay is there a chance the basic graphs can be realized in two colored and or weighted graphs it's impossible to considering okay let's let's take those first okay so the equivalence between different different kinds of of graphs yes absolutely you can so a lot of what hurts if I can share screen here um a lot of them I tried to to talk about that a bit in section seven here equivalents so there is there is equivalence between both so first of all we are often considering hyper graphs where there's a hyper edge that is a ternary hyper edge for example that we're representing like that it's an ordered ternary hyper edge but there are there are lots of different formulations that one can give of this so for example one that was actually my earlier formulation from the 1990s was trivalent graphs and there's there's a ultimately you can represent any trivalent graph transformation rule in terms of hyper graphs and vice versa but with more and more complicated constraints to make sure that you you you stay in the same class of graphs of hyper graphs but yes the one of the things that sort of disappointing to me to discover is the stuff that I was doing in the 1990s on trivalent graphs it basically gives exactly the same results as we now get with this in my opinion more elegant formalism with elements relations hyper graphs and so on but yes there's a there's a close correspondence between between all of these kinds of things so energe hyper graphs I think that that is what we're what we're talking about here is a hyper graph with with with for example you know ternary edges or whatever else um let's see is there a chance the basic graphs can be renormalized into colored and or weighted graphs so yes there are in fact this is yet another model here which again I talked about the equivalent this is this is a kind of an ordering scheme where each node kind of has has an order to the edges around it but the edges themselves don't have directedness so that's just another kind of kind of graph like thing could you do this with colored edges I'm I think the answer is definitely yes haven't actually done it I encourage you to do it you should be able to see the correspondent why do we care about all these different reformulations the answer is in the end we're going to be enumerated and these different reformulations while ultimately equivalent will enumerate the rules in different orders so it could it could be that a sort of colored network model will be the one that enumerates in the order that lets us find rules for physics sort of earlier in the ordering than than something based on hypergraphs for instance we just don't know that yet I have been was really keen on this elements and Relations approach because I just think it's it's very clean and it sort of meets my criteria as aesthetics the universe might not agree with me so to speak it might be that for the universe the the you know the colored graphs are the ones that are will enumerate most easily so another pistas question is it possible to consider a single ordering of updates randomly selected from full branch real space and create a stochastic hidden variables theory where that is the only state that happened okay that's it that's a very good question we have actually in our we have this wolf model function that let's see if we can pull that up here tools let's see this is Max's code and guide to functions and I will show you so here's this function and this has yeah I think we can look at it here um this has thee where is it event ordering function how to order possible updating events so the event ordering function determines exactly what you're talking about and one possible setting the event ordering function is random okay and so that means that in that in the usual way when we run these models were usually only okay before we look at multi way systems we are just looking at a particular ordering but this allows one to try out random orderings and so the question the this you're absolutely right that that's a good point actually that um stochastic hidden variables theory would correspond exactly to your picking a your randomly picking a single path through the multi way system now an interesting question is whether some of the work by I don't know you know Nelson and those guys on on stochastic and variables whether we can specifically apply some of the mathematical ideas from that to the case of a a stochastic elite Rosen branch and multi way system how about Jonathan do you have any thoughts on that not really I one thing I would say by the way is that another way you you can you can effectively apply a sort of stochastic event selection process is using our multi way system code with an event selection function set to random and and so then so where Mac says willful model code does effectively generational evolution updates so you're playing kind of maximally consistent sort of sets of space like separated updating events the multi way system code works in a fundamentally different way it only applies one updating event at the time and so then if you want to apply genuinely a completely random updating event for a given hyper graph you can use the multi way system code in order to do that's and actually visualize the whole convolution tree the question of whether we can get a stochastic hidden variable interpretation by using effectively you know random event selection functions as Stephen says it's an interesting idea it's not one that we've really considered but possibly a light string good topic for a live stream let's let's find the world's expert on stochastic um hidden variables and let's get them to join us and we'll talk about that it's a good idea and it would be a good thing to analyze um and maybe maybe the person who asked this question is an expert on this in which case please let us know and we'd love to chat with you further okay next question here was an unpronounceable handle here so sorry unone C ROM age-old continuous versus discrete question remains can this model account for what some believe a continuous phenomena yeah the answer is yes we absolutely think so and essentially that's happening through this limiting process just like discrete molecules bouncing around can appear to be a continuous fluid in standard statistical mechanics so we have the same kind of limiting process that by the time you have you know 10 to the 100 nodes in your discrete hyper graph it behaves an awful lot like a continuous space and that's the idea now let me mention one very very bizarre possibility okay about can discrete versus continuous so imagine that the underlying hyper graph is it has an update rule that is continually essentially generating new nodes so it's continually sort of subdividing space into finer and finer pieces so here's a bizarre thing that could happen you could say I'm an observer of this space I'm going to go and make a measurement in which I prove that the universe is discrete but during the time effectively that I'm setting up to prepare that measurement the universe could have subdivided further so in a sense the the discreteness of the universe is continually receding from you because every time you try and probe it it's it's getting more fine-grained so that would be a a to me that would be a very interesting conclusion to the sort of 2,000 plus year debate of is the world continuous or discrete is well it's actually discrete but you'll never know it because every time you try to probe that discreteness it's going to subdivide and get away from you and it kind of amuses me that term I never was a big fan of epsilon-delta proofs in calculus but it's a it's a literal the universe is literally doing one of those epsilon-delta proofs and showing that it is a continuous limit Jonathan looked like you had some comment on this no no I just I really like an explanation that was well okay all right this question from Joe Crowley um where are the spinners yes we we are about to go look for the spinners the fur so um I mean that is a a very the question of what the effective rotation group is four four particles basically and whether that is so3 or su two and how we get the spinor representations out and so on that is actually that is going to be one of our first working session livestreams is talking about spin and spinners and so on Jonathan thought he had some partial answer to that but Tim I'm not sure we're not yet sure about that I do want to do want to say something about that charlie yeah sure so one yeah as Steven kind of mentioned we the answer is we don't know but one way that you can get mathematical objects that are actually very much like spinners is actually is it's a very natural thing when you consider the geometry of branch eel space because so as Steven was talking about yesterday when you look at these different branch like hyper surfaces that kind of divide up your your multi way revolution graph you can look at how gd6 in the in these in in front chill space are turned as a result of the action of the multi way system and that turning gives you a kind of angle and that turns out to be the angle but we think it sort of enters into the into our derivation of the path integral but here's an interesting thing so in general these multi way systems they grow over time right they very often they grow exponentially or even super exponentially so one branch like hyper surface could be much larger than the previous one the result is that actually it means that things can turn through much larger angles than you'd normally expect them to be able to turn through and so what you look at one geometrical intuition for what a spinner is is it's like okay you have a vector space and it's equipped with a representation of the spin group and then what you have at least spinners which are elements of the vector space with but with this bizarre property that when you turn them round by 360 degrees they negates so in fact you have to turn them 720 degrees to get back to where you started from so there's some kind of square root of ordinary geometrical vectors it turns out those are a very natural thing in branch real space because you can have objects that appear to turn 360 degrees and be facing in the other direction effectively because the branch eel space is continuously expanding and so the hope is this would give us some intuition about the natureís then we as I say we I think Stephen and I both have conjectures about what spin might be we might discuss them later on but that's something which you don't need to figure out right this is this is this is a great topic for one of our working session live streams coming soon okay next question from K key key a can we derive the Fineman particle formalism from the theory yes yes we we believe so and it's very beautiful and it's basically it's kind of I think it's fair to say it's kind of the analog of Einstein's equations in branch real space and that's kind of the way to think about it it's the effect that Lagrangian density has on gd6 in much the same way that in the standard Einstein equations are talking about sort of the effect that energy momentum has on gd6 I don't know whether we can I mean I think Jonathan I think you have a pretty formal derivation of the path integral in your paper right right right so it's yeah so Stephen says I mean the these these multi way evolution graphs they're you know if you stop think about been into it sort of intuitively they seem very much like a like a possible to go like they are some kind of some of the history's type type thing yeah so so as Stephen said if you then try and define effectively continuum equations on Brancheau space you get some analog turns out you get some analog Afghanistan field equations where the what would normally be the space time metric tensor is replaced with this object called the through beany study metric tensor which is this sort of geometrical object that's used in studying projective Hilbert space it's kind of the natural curvature metric on projected hilbert space and it's used as a way of because of quantifying entanglement distance between quantum states and things like this and so with this information you can affect that you can equip the the multi way evolution graph with this measure which you can then sum over and then the claim is that you know again in using the same assumptions that Stephen mentioned for the Einstein field equation you basically have to assume certain amounts of microscopic randomness in the evolution of multi-way evolution graphs but assuming that happens in assuming you can make some weak Gerda City assumptions that discrete sum over this measure of the entire multi evolution graph converges to an integral and it converges to an integral with basically the same form as the Fineman patterns but that's more or less how we think quantum field theory might work in these models you know one question that came up yesterday from I think a question on the live stream was was whether this approach would give one a new way to actually compute an approximate path integrals and that seems to me to be a rather interesting idea because what we're realizing is that the approach to looking at the Einstein equations and looking at space-time using these underlying hypergraph models and so on actually gives one ideas about how to do numerical general activity and maybe we can I mean it's it's sort of a long-term issue how do you find good numerical approximations to path integrals and it's not something one normally does I mean one can make lattice theory but that's an equal in space-time and this might give one a way to do in rakov ski space-time a way to do a discretization of the path integral any comments Jonathan on that no that sounds perfectly reasonable Steven knows much more about path integrals than I do I I have a few ideas about how we can use these techniques for doing better numerical gr but numerical QFT that's I think that's that's your ball game well what what talk about the numerical derivative case because okay yeah yeah sure so okay so actually we discovered recently that you had a note to this effect at the end KS book that I had not remembered apparently no that had you that actually these causal graphs might give one in a new way of do it of setting up some initial value problems for some Hamiltonian gr so you know one of the conventional ways that you would do that okay one of the reasons why a numerical relativity is hard is normally if you have a system of you know hyperbolic equations or something like in fluid mechanics and you want to solve them you you cast them as a time evolution problem and you can do that in fluid mechanics and in most equations but with general relativity time is part of your metrics you can't there's no obvious way to do that so what you basically have to do is foliate your space-time into these according to some parameter that's like a kind of fictional time parameter and then and then do it and then define your initial value problem on those hyper surfaces and that's how these decompositions like the ADM decomposition and the dsm decomposition the people use in the american journal relativity as how they work causal graphs and this notion of causal graphs the limit to the continuous space times gives you the this notion gives you a kind of a much less structured way of potentially doing the state of potentially doing the same thing so you can use a causal Roth to recast the anagen equations as a as a sort of initial value problem except now rather than in some standard numerical general relativity cases where you have a you know you're you have some curvilinear coordinate systems your neighborhood structure is very well-defined as you know normally you have every cell in your space like hypersurface has six neighbors in our in the context of our causal graphs because our degrees are unconstrained you can have cells which have arbitrary numbers of neighbors and you can have a fixed really flux is coming from arbitrary different directions so it's a kind of it's a grand generalization of these techniques of numerical general relativity that I think is going to be really exciting and potentially really useful for people for you know astrophysicists cosmologists and people working in those kinds of fuels and if we can do the same thing for quantum field theory you know that's gonna be really awesome you should write up the thing with numerical relativity that will be very useful to people okay they um somebody is asking what is Jonathan's background okay Jonathan young would happen computer science you know and got a background did the DC mean we don't know whether the background is the clock or whether he means the background whether this might be spatial or temporal or something okay I'll give very brief answers to both questions because we were actually just before the livestream we were discussing the I have a pneumatically relevant background from discussing the nature of time it's big sort of a giant pocket watch behind me so okay if you meant my academic backgrounds I was sort of I was trained as a mathematician I my my background is really in kind of differential geometry and things related to the mathematical foundations of general relativity so things like I'm particularly interested in tensile methods and certain techniques for hyperbolic partial differential equations and things like that but I'm kind of I have interests all over the place i I've also done a fair amount of research in areas like computational complexity theory and graph theory and in foundations of quantum mechanics and actually the work I do here at here at Wolfram is in a weird combination of mathematical logic and quantum computing so I have I have a few it's kind of nice that there have been a few different domains of expertise I've been able to call on in the course of this project I think it's really amazing because a jonathan has worked on as you mentioned graph theory general activity automated theorem proving and quantum computing because that there's a know in areas that that I know Jonathan's worked on and they all turn out to be relevant to this project which is which has been rather cool ok um what exactly Andrew on Twitter reading through this what exactly using four elements in the actual software to display these are these just coordinates on-screen you draw a line to each coordinate within loop I'm not quite sure what that means I think I think you're asking how do we determine how to actually lay out one of these hyper graphs on the screen we're using sort of well it's it's it's Wolfram language graph layout the Wolfram language graph layout system which in turn is using algorithms with things like spring electrical embedding where you're imagining that the graph has a bunch of nodes which are connected by Springs and which electrically repel each other and one of the issues is sometimes you'll get stuck in local minimum in in Visio you're making essentially a an almost physical model of what this graph will be like if it was made from Springs and electrical repulsion and things that were electrically repelling each other um and sometimes you'll get a physical you'll physically be stuck in a in a state where which is not the which is not the true minimum state and and you'll see actually to my great frustration in my paper for example there were a few places of fold overs that we had a hard time resolving we mostly were able to kind of essentially shake the this sort of physical representation of the graph for purposes of rendering and get the fold over to not fold over so to speak particularly for for graphs that have sort of exponential growth as you go towards the edge that was hard to do um one of the things that we've been interested in is having a more interactive system for understanding these graphs by having them in in for example virtual reality in fact we are in the process of building a system we'd love to get help on this it's building a system primarily in unity game development engine where you can actually go into sort of virtual reality and meet your graph and with your hands move pieces of the graph around and have the thing automatically adjust and for real major bonus points be able to see the evolution of the hyper graph right there in virtual reality and see the thing one of the things we haven't solved we tried to solve we didn't manage to solve it is if you have a single graph and you want to lay it out well that's one thing you can do it with these kind of physically based methods but if you have a graph which is progressively evolving being able to have sort of correct correspondence between different stages in that evolution and having each of those stages be consistent we really haven't solved that problem so an analogy to that problem is the problem of looking if you look at a bunch of soap bubbles and the soap bubbles are gradually changing they're the the edges of the soap bubbles to form something like a graph and you know soap bubbles will gradually eventually a soap bubble will pop and then the rest of the graph that represents the the boundaries between soap bubbles will will move around or adapt to deal with the fact that the graph structure has changed we would like to have something a bit similar to that in representing kind of the dynamics of one of these hyper graphs but we haven't solved the problem of how to do it and it would be wonderful if someone could could help with that and if we're really good where we're actually our our graph theory team research was said yeah they'll try and come up with some virtual reality based system for doing this graph layout thing but I think that they're busy doing other things and we'd love to get to we'd love it if some other people were interested in helping with that and we're happy to provide the code that we have so far for for doing that but the end result will be to have something where you can really kind of live with your graphs so to speak and be able to manipulate the moment we'd like something where you can I think I think one's fingers are probably going to be a really good way to have an interface to I think it's actually going to work better than for example the typical you know game controller type things I don't think that so I think what's gonna have to pick up the graph and pluck it and put it somewhere I think that's going to be a little bit awkward woman has a game controller man has to hold some button down to to it to pick the thing so it'll be good to have something which has some more like a thing that can actually sense finger locations and so on okay let's see okay question from nil and hacker news model seems very flexible to the point where I'm unsure that it's surprising to be able to recover generality and other properties but sayings that but adds depth but given the depth but but given that string theory seems to face a similar problem of model selection have you looked at equivalences between these and does that make sense in your eyes so so the whole string landscape thing is really not an issue that we have I mean that's it that's a that's a strange feature of string theory and and it's just it's problems that the appearance of general relativity is in my opinion really quite non-trivial it might not have looked that way I mean it really doesn't it is the fact that it turns out that general activity is generic to a wide class of our models is I think a statement that we're really kind of on the right track in the structure of these models I mean one could easily for example let's imagine let's take as a kind of a null hypothesis or something let's say we're going to make a cellular automaton reproduce general relativity it's gonna be really hard it's basically just not going to work it's not going to work to reproduce special relativity it's not going to work to reproduce general relativity so that's a case where if you want to say is there content here the answer is well it certainly might not have worked I think there's real content and saying that it worked um now question about the string landscape do you want to Jonathan do you have any comments about string landscape about the landscape in particular not really about connections to string theory which I think was the second part I think we both have things to say but I mean do you want to do you want to take the well yeah right I mean a lot of snakes take place so so again we're hopefully we will do some live streams with some you know sort of people who are in this true strength ferry business who do string theory for a living we actually had a discussion before we launched this project with it with a group of string theorists um the I think I strongly suspect that string theory and it's mathematical structure represents some limit of some corner of our space of models but I think actually it's probably not our standard hypergraph models I think bizarrely it's probably a limit of string substitution systems which are kind of a you can reproduce string substitution systems from hypergraphs but they're not particularly natural from there but it's something which is is is kind of easy to look at where you're just dealing with strings of symbols and the question is which I have long wondered about actually is what is the continuum limit of string substitution systems and the bizarre pun like possibility is that it might be string theory or string field theory but that really has to be investigated and I think it's a it's it's just a it's a really interesting thing to look at independent you know string substitution systems have a continuum limit we don't know what it is and you know it might be string theory it might be something different but you're just investigating the continual orange with string substitution systems is immediately an interesting mathematical problem did you have something else you wanted to add yeah well let me let me give to make to make it seem like it's not just based on a pun to make it clear there is actual substance here let me let me give a kind of very conjectural outline of how that might work so we have okay if you consider a multi-way system whether it's a multi-way system for hypergraphs or multi rate system for strings it kind of doesn't matter you have all these states in there and their branch like separated but some of them are kind of purely branched like separated in the sense that the updating events actually overlapped with each other and produced ambiguities and some of them are actually just space like separated right there were there were completely spatially independent events that just happen to lead to different outcomes and so all if you have causal invariants or if you have sorry if you have basically if everything is in causal contact then all the space like separated updating events will eventually converge and that the answer the essence is the essence of the multi way branching of these branch light of these purely branch like separates it's updating events okay so one thing we realized was in addition to having this this full multi way system we could invent this thing called a generational multi way system where basically at every step we apply a maximally consistent set of space like separated update events so that the only branches we see are the pure branch like separations and so that so then that this gives this gives us states of this generational multi way system which we described as being snake States and the reason we call them that at least informally call them lats and some of our material is because if you can you can track them in the normal multi weight system because all you have to do is track the subset of states that were produced by purely space like separated events and that for a string substitution system that will be a 1 a 1 dimensional extended structure in the multi weight system then those snake States that yield these generational multi-way states they have you know that they can merge they can splits that they have they appeared to have kind of sort of propagator type behavior and at least in toy examples it seems entirely plausible but actually that those are the those are acting like world GDP so that the history of those snake States act like world sheets in string field theory and those joining and merging operations of the generational multi way system are actually the the joining and merge the yes sorry the merging and splitting vertices for the for the string field 3 propagator I just wanted I was just gonna find a snake yeah yes yeah this is gonna make it much less this is gonna make what I said much less obscure right so that there's an example of a snake this is in the branch Hill grass and that is the that is a snake state in the branch show graph um and I think I think Jonathan I know whether you ever did this whether you whether you end it ended up with a section of your paper called snakes on a plane I was very tempted but I can you advise me not to fair enough um but yeah so that the notion would be that's the worldsheet basically that's the evolution of the worldsheet corresponds to the evolution of the snake state through through through time in the successive stages of the broad shield graph so that's the idea there okay let's see next question was from ninja of lu where does distance come into this I don't think I caught another thing about it in your article only rough length scales where do those come from okay well let's let's talk about that um all right what is gosh what how should we describe what is distance um let's my might have some nice pictures here I don't yet know my my em here we go alright so so distance the the simplest measure of distance in space on the spatial hyper graph is the graph distance between points so that means if you're going from for example this point to this point you're asking what is the shortest path through the graph to get from one point to the other that's that's the notion of distance that is the simplest notion of distance that we have in these hyper graphs and that's a well-defined notion of distance it satisfies all the all the sort of standard axioms that a distance should satisfy now is that the true physical distance between those points really when we want to measure distance in the real world so to speak will you do things like send a light signal from one place to another so it isn't really the case that it's just a question of what path on the graph exists it's a question of how does a photon get from here to there well in our model a photon is just part of the graph so certainly a part of the story of how photon gets from here to there is it's propagating through the graph it's it's making use of edges in the graph but that's not the whole story of how you get from here to there and so it's it's slightly more complicated to say what is the what is the what's the what's the distance as measured by a photon as opposed to what's the abstract distance in space this is talking here about the abstract distance in space we can also talk about the distance measured by photons but it will be related to the distance measured in space so I think that's that's kind of the and in terms of what is that actual distance well in what we're looking at in the end is is we're looking at causal graphs that tell one for after one unit of elementary time one will be sort of connecting two points in space and the the the sort of conversion factor of 1 unit of elementary time how far is that and physical space well it's about speed of light times that our mantra time that sort of the way of of setting the dimensions setting the units for for that distance let's see um okay so from yep jayveer here Lopez would like to know what are the nodes of the hypergraphs exactly are they nodes of space basically yes I mean they're abstract elements that are what make up space I mean I think that's the best way to say it and they're not only what make up space they're what make up everything in the universe they are everything in the universe is made of the sort of set of relations between these these nodes in hypergraph so that means when we have a particle for example it must arise because of sort of the the the the pattern of connections associated with that between these particular nodes in the hyper graph um is it correct to the moe you're proposing must be from Bernard grass on Facebook is it correct that the model you're proposing must be multi way yes yes it is it is for any non-trivial underlying rewrite rule it will be the case that there are ambiguities about how that rule can be applied and the result of that is that the way we're representing that is through this multi way system and that has the feature that well as I say any non-trivial rule will have that property that it has this ambiguity and we're saying that that means that you have to follow all the possibilities which leads to a multi way system and what's really nice about that is it inevitably leads you to quantum mechanics which i think is and it sort of explains you know why is there quantum mechanics why isn't the world made of of what why why is it not the case that classical mechanics can govern our universe well the answer is in this model it's just inevitable that you couldn't make a universe that was purely governed by classical things that had non-trivial that that would work actually interesting question which I'm now wondering about could we imagine a a model like this I don't think we could I think we could not imagine a model with sort of computational irreducibility cause on variance all these kinds of things that has the property that it would be a purely classical model Jonathan any thoughts about that I don't think it's possible I think what Barry proved that that's not possible in other words we could prove that the multi-way nature of of progression through time is necessary in order to achieve a non-trivial universe that there is only only trivial universes could satisfy purely classical mechanics do you believe that Jonathan I think that's probably true yes I need to think about exactly how you prove that but the one possible way you could is we know that the sort of the word problem in computational group theory is is formally undecidable and effectively the reason it's formally underside of all is because if you try and decide the word problem you have to tree out this whole multi way system of possible kind of group derivation for you're finally presented monoid and and the fact that you have that multi-way evolution and that in particular sort of multi way branches can extend it infinitely is the reason why it's undecidable so I think the converse of that would say if you didn't have a multi-way evolution and the word problem would be decidable which we know that it's not so I think I would put it differently I think the point is that that what you're saying is as soon as there isn't multiple evolution the word problem is decidable and then we have computational or irreducibility and you can't have the universality I think you again prove that your universe can't have any richness to it so that that's okay interesting interesting result this is this is some kind of what we as sort of the point of having an open science project so to speak is that people will raise these kinds of questions which let us get to interesting results Thanks um some of the notes aeration general today yes thank you we think so okay are you able to show how to derive Maxwell's equations from your model from James good question okay so the sort of the closest so to derive Maxwell's equations we need a notion of electric charge um and we don't yet have a notion of electric charge we think that electric charge will be associated with essentially so electric charge probably okay here's an interesting question that we don't term um the that we don't have actually this is a this is a good question we don't know if there is a bulk notion of charge I have to say when we came into this project I didn't think we were going to be able to define energy in a kind of bulk way that wasn't dependent on looking at the properties of individual particles okay and to my surprise we managed to figure out that energy is a flux of causal edges through space like hyper surfaces so now the the exercise is is there a bulk definition of charge and because what we've been thinking is that charge is associate you know what I bet there is okay so so I mean charge is normally associated with particles like electrons have charge minus one and things like that charge unlike that there's a there's an immediate quantization of charge that we know exists for physical particles charges have particles all have multiples of the one third electron charge charge that quarks have or at least that's how it appears right now so the question of so actually that's a really good question whether there's a bulk way to understand charge in our models and I I'm kind of kind of guess that it has some topological character that is like that has some discreteness for some topological reason like it's it's some pontryagin index or something or something something like this which has discreteness because okay so the answer is we don't really know the answer but the what I had been thinking before being stimulated in a slightly different direction here is that what we would have to do is to reproduce local gauge invariants so one thing to say Maxwell's equations were the original place where the idea of local gauge invariants arose where the idea of being able to say it's kind of like you can set the zero of voltage anywhere you want you don't have to say what what is zero volts well you know what is the ground for a circuit you know you can kind of set that arbitrarily and you can set it differently in different parts of space and that that freedom to set it differently in different parts of space is local gauge invariance and one of the features of local gauge invariance is it implies the existence of photons and it's not too hard to give an argument for that but the I mean okay I give the argument just for people many people may know this argument imagine you have an electron and the electron is producing an electric field the electric field kind of looks like no it's like a hedgehog streaming out from the electron and okay that's absolutely fine now let's say you move the electron okay so far away from the electron the electric field has to change that Hedgehog has to be displaced the question is how does that displacement how does the fact that you move the electron how does the information that you move the electron propagate out to the sort of outer edges of the hedgehog so to speak and the answer is it propagates out through having there's a there has to be some sort of the analog or massless particle a photon that is sort of propagating that change out to the to the sort of distant places where the electric field is showing up so anyway the the the sort of the derivation of Maxwell's equations would normally come through showing the u1 local gogo gauge invariants we have ideas about how to establish that local gauge invariants but I am now thinking that there is a bulk way to understand charge and I bet it has to do with see the thing is that normal topology doesn't really apply to our hyper graphs we need to generalize normal oceans of topology okay Jonathan I'm gonna throw this money at you do you have any ideas about about sort of what the what some analog of something like a pond tree organ index so one of these are betting numbers or something like that would be for these hypergraphs that term not not right now I need to think about it I mean it's it's actually it's a really interesting idea it's it's something it's it's quite similar to something we discussed I think a couple of months ago about a possible way of thinking about charge which was that you know within within the models as we've been thinking about them the energy-momentum tensor as Steven mentioned is basically this this flux of individual causal edges each of which corresponds effectively to the updating of a single hyper agent in the hypergraphs but you can also think about fluxes of kind of configurations of hyper edges not just single hyper edge configurations but kind of you know configurations of three hyper edges and you could flex those and things like that and and kind of you can imagine having more non-trivial topological structures and convinced of classifying fluxes of topological obstructions and things like this and wondering I have an idea what we should look at the cycle structure of the cause of these graphs because I think that's a that's a place where one can imagine see see what you're suggesting there is when we look at fluxes of individual first point when you're looking at fluxes of individual causal edges that's basically a vector field type story and there's a question of as you're mentioning there's a question of when you're looking at multiple hyper edges attached to a single point you're looking at essentially the flux of higher order tensors so one first question is what is the analog so just as if energy is a flux of causal edges through space like hyper surfaces what is the flux of pairs of correlated causal edges through a hyper surface and so what's the higher-order analog so I think what that that would be the first level of thing is a higher order analog of T minou higher order analog of the energy momentum tensor so that's a question what would that be that's going to be higher order derivatives applied to the distribution of energy momentum so to speak so first question so there's a generality question what is the what is the higher order version so I mean given that you have a star for example and the star has some distribution of density and so on there clearly is a higher-order generalization of pure team you knew for that what is it I mean I guess I guess at some level its derivatives of Chimney new but what's not obvious to me is that team you knew on its own so so the the claim would be yes here's the claim the team II knew probably is the way it is because a bulk material is characterized by pressure and energy density but that is an approximation so if we think about a gas for example the the saying that a gas is characterized by its pressure in its yeah the way to think about that is this the so to say that a gas is characterized by its pressure in its energy density is to look at the one particle distribution function if you're looking at the multi particle distribution function you have more stuff and so that's going to be what the our law goes the analog is if instead of team you knew you're looking at the correlated the team you knew is a way yes okay I get it so T mean who is is what you get from from looking at a material and saying I'm gonna scale up the material and I'm gonna look only at the one particle distribution function if you were to look at the two particle distribution function which you could do in a gas and in the very expansion for example you would get things like that um then that is but that but to say that you're looking at the two particle distribution function is to admit that your material is not a truly bulk continuum material it's to admit that it's made of molecules and you've actually got some some underlying sort of correlation between those molecules so I'm I'm kind of gonna guess that what's gonna happen is oh that's interesting it's it's some that it's it's going to have when you look at this higher-order piece it's going to be something that actually cares about things like you know Branch Hill space and so on as well as caring about physical space but I think that's a it's an interesting idea to think about what's the generalization of team you knew in a case so I would suspect in kinetic theory in relativistic kinetic theory the people have tried to generalize yeah is that a fact I worked on this 40 years ago okay the it's I wanted to know what the what the generalization of so standard the standard gas laws PV equals NRT or whatever the question is what is that like for a relativistic gas and then what is that like for relativistic non-ideal gas what does it even mean to have a relativistic non-ideal gas and the answer in that case when you thought about in terms of particles was that the it's directly related the corrections to the gas law are directly related to phase shifts which come out in the S matrix in the scattering matrix so in other words when when a gas is non-ideal what it means is that the the particles the gas aren't just elastically bouncing off each other they're kind of delaying before they before they go on so I think there's okay so I'm predicting that there's a there's a direct sort of connection between this sort of aerial expansion for the non ideal gases sort of higher order Corrections multiple okay this is an interesting thing to investigate all right sorry we're generating homework for ourselves or for or for other people here um but but so I mean I think the bottom line is I'm gonna guess that charge is we should really look at this I think they're going to be some things about cycles on the graph or some other graph theoretic thing in the pet that doesn't require the the that some other sort of graph theoretic characterization which is going to have and the we've already got a clue cuz we know about quant the quantization of charge and that's presumably a clue which tells us that for example it I mean you know there'll be some things which for example the question of whether a cycle closes maybe an answer may be something which is a sort of a or some question about whether if you have multiple cycles whether they can be not there this there's probably a an algebra of cycles that will be analogous to stuff I don't understand very well in Holland ami and things like this and of curves in in mathematics any comments I just wanted to make one quick comment about how this this sort of general idea of you know considering larger scale sort of structures of causal edges and there and there fluxes through the causal graph how that sort of Nestle's with the ideas we currently have about local gauge invariants so one of the really nice features of as Steven mentioned in Omak Maxwell's equations this whole idea of you know out of the equations of motion for chart for electric charge this was the first real hint in the history of physics of this concept of local gauge invariants our current ideas about local gauge invariants are that ok when you have one of these hyper grasses as I mentioned earlier you can think about when you're revolving just the pure Wolfram model case not the multi-way case what you care about are the kind of maximally consistent sets of space like separated updating events the crucial point is because of the hypergraph structure where you apply the first updating event places constraints on where you can put the other updates you've got like a kind of jigsaw puzzle tessellation problem do you have to solve at that point so it's like your initial choice of where to apply the update which hyper edges to include anymore update is like a choice of a local coordinate frame in fact we can make a sort of precise mathematical correspondence here in terms of thinking about gauges in terms of connections on a gauge choices in terms of connections on fiber bundles so you can think about the hyper graph as a fiber bundle and and say each each individual node a hyper node corresponding to a fiber with the with the different kind of edge orientations corresponding to local gauge choices but then if you have if you make a more complicated gauge choice that involves more than one hyper edge that's then going to be constrained and will in turn constrain how causal how pair y is sort of causal edges can get flux through the causal graph and I think that's potentially how we're going to be able to derive something like Maxwell's equations but that's there's a lot still to be figured out there right but I think this is a good idea we had not really thought about charge as a bulk quantity and we need to think about that and I think there's I think there's something interesting there thank you then ok let's see a question from naman Agarwal fundamentally is your model like loop quantum gravity let's see well Jonathan you understand loop quantum gravity why don't you why don't you talk about that ok sure so the this there's a I can give a longer answer to this if people really care but let me first give the only give the short answer which is there's a sense in which it's like with quantum gravity and there's a sense in which what we're doing is fundamentally different so the similarity with LQG is in lqg people care you know one of the really nice features of LQG is that it has a combinatorial representation of space and space-time which is of course very similar to what we're doing so in LQG what you have is the structure called a spin network which is a way of representing the quanta if you have a if you have a spacetime you divide it up into these three dimensional space like hyper surfaces and you want to define the gravitational field on each of those hyper surfaces there's this combinatorial structure that represents the quantum state of that gravitational field and it's kind of entanglement state and that's called a spin network and these kind of fundamental objects of LQG and then when you consider the whole of space-time that combinatorial structure gets replaced with this higher dimensional object a topological too complex as it's called that represents the quantum state of the gravitational fields across the whole space-time and that's that's this thing called a spin foam and so in a sense of spin foam is what you get when you evolve a spin network through time and this is actually you know from the point of view of doing physics into thinking about physics in terms of combinatorial structures this is very similar to our notion of you know start with a space like hypergraph and then kind of evolve it in time and you get this this causal graph structure but at a mathematic so on the surface they they have various features of the formalism in common and actually I hope is that some of what we have a sum of what the LQG people have done will be useful in what we've been doing and hopefully vice versa some of our insights we hope will also stimulate some research in lqg the the one key point where what we're doing is fundamentally different is in the case of a spin Network the edges actually mean something right in the sense that each edge represents an irreducible representation of a compactly group well and that compactly group is kind of is or is already defined and the vertices then correspond to the to the intertwine as of the adjacencies and that in in you know the adjacent representations of that compactly group so the point is with our models we haven't we don't we don't define a compactly group a priori right all of the kind of algebraic and symmetric features of our of our models emerge purely as a result of the discrete underlying hyper graph dynamics so we're in some level what we're doing can be considered a significantly less a significantly more structureless version of what people were already studying in RPG that's my short answer isn't isn't it the case that in that there's a background space-time effectively I mean there's a you know these these spin networks or embed in three plus one dimensional space yes right so this is um okay that's that's a good point that's another good it's another sort of crucial place where we're what we're doing diverges without qg and also where it diverges with other kind of combinatorial representation idea it's like in like in causal dynamical triangulation of other kinds of things all of these models as Steven said basically assume you have a background continuous space-time and then you do something you and then you decompose it you usually you do this topological operation called a simplicial decomposition you decompose it into what's called a simplicial complex where you're just kind of tessellating in space with a bunch of these simple topological objects called simplices and then that gives you a topological structure this combinatorial structure which then is supposed to represent the quantum state of the gravitational field or something like that we're kind of doing the opposite thing right we're starting with the combinatorial representation and we're kind of we're evolving it to us to a point where the the continuum background space-time actually emerges as a consequence of the combinatorial structure as opposed to the other way around that's that's a good point that's a little light actually we if you didn't have that in your Q&A answer but LQG you should probably put that in there yeah I'll make it out now no I mean sort of to sort of summarize that difference I mean you know in lqg one starting from the assumption of continuous space-time and then and then saying let's let's put you know let's discretize that existing set of you know dimensions of space and time whereas we're we're saying just start everything from this hyper graph you you haven't committed to three plus one dimensional space-time ok how do you get continuous some aged bronze on Twitch how do you get continuous geometry when looking at most of your example models you have a grid like structure which only has a finite number of dimensions okay some other cellular automata where you got Manhattan distance geometry you always get finite number of dimensions okay so the the answer to that is it is the case that some very simple examples have grid like structure the more generic case is that there's great randomness in the sort of in the structure that statistically the thing is let's say two-dimensional but the actual detailed structure is not in anywhere you're absolutely right that if you had a pure grid you would have Manhattan distances and not standard Euclidean distances but the generic cases that there's microscopic randomness effectively that leads you to have something that's much more like a random mesh on which you have an approximation due to gradient distances um okay a question from the via Lopez we've been able to derive other equations like Maxwell's equations consistent with physical laws we talked about Maxwell's equations there I don't know what what what else is there in physics let's see there's I mean you know the standard model has okay let's let's go through the inventory of what's in the standard model it has a certain set of particles it has a certain set of local gauge invariance --is it has it has some well has spontaneous symmetry breaking it has the Higgs field and the coupling to the Higgs field and we haven't thought much about the Higgs field and spontaneous symmetry breaking yet the Higgs field is kind of the modern ether so to speak in the sense that the the way that you know in standard in the standard model the way that particles get mass is through their being a nonzero vacuum expectation value of this Higgs field and that you know in our setup where we're building space as part of our model this idea of a vacuum expectation value has a slightly different character and needs to be thought about so another thing about the standard model that is perhaps interesting to look at is the off diagonal elements of mass matrices and things like CP violation we mentioned yesterday which has to do with complex terms and which can be thought of in terms of complex terms and mass matrices things like that those are things that as we start figuring out more about particles I suspect we will see examples where there are off diagonal terms and mass matrices and things that also happens with neutrinos um okay shoo mush on YouTube can this explain the segments of thermodynamics it is just great that people are asking about the second law of thermodynamics I thought nobody had thought about the second law of thermodynamics anymore because the second law of thermodynamics was one of the first sort of foundational physics things that I got interested in when I was 12 years old and I've been interested in the second law of thermodynamics ever since then and I think finally in the 1990s I kind of figured out why the second law is true and the fundamental answer is the second law is all about taking okay let's be a little bit formal about the second law the the issue is that we believe that the microscopic dynamics of physics are reversible in the sense that they're not they're not it doesn't happen to be exactly the same operator for forwards in time as backwards in time but it is nevertheless the case that states are mapped one to one from the the set of states that you have as you go forward in time is a one-to-one mapping as you go forwards in time so you can always reverse the set of states okay so given that every state has a unique successor every state has a unique predecessor how can it be the case then that we get what we observe in the second law which is that you start from these kind of simple looking States and you end up with these states that's that seem random or put in a more formal way seem typical of the ensemble of all possible states okay and the way this was very confusing this is what you know from 1871 Boltzmann did his H theorem and so on this was the reversibility objection this was always the confusion of how could you show that entropy increases when there is this microscopic reversibility and what what happened in Boltzmann's proof was that he was effectively assuming molecular chaos he was assuming that molecules would be uncorrelated before they collide but then inevitably they become correlated after they collide and that's where the sort of the the asymmetry in the proof comes from but so then people like Gibbs tried to work out sort of a more mathematical formalization of the way that the second law works and what Gibbs introduced was this idea of coarse graining the idea that you even that that when when you look at all these particles and they're all bouncing around that the only thing you end up measuring is the approximate coarse grained positions of all the molecules you don't get to say this was the particular can okay so the thing to say if you knew that if I knew the precise configuration of all the molecules of air in this room and the room was perfectly closed and so on then in principle I could sort of run the movie in Reverse and I could work out where the molecules were yesterday and for example in particular if all the molecules have been in one clump in the middle of the room and the rest of the room was a vacuum and everything had expanded out I would be able to reverse the movie and find out that the molecules came from that small clump in the middle of the room and that would be kind of a a in so why can't you do that so Gibbs had this approach of saying well because you can only make coarse-grained measurements you can't actually know the precise positions of all the molecules you can only know coarse-grained versions of that okay so I sort of figured out a more precise version of that statement that I think is really the the thing that is the sort of provable version of the second-order thermodynamics and the more precise statement is that oh by the way when you talk about coarse graining people got kind of confused because like how complicated think on the coarse graining be is it really just lumps in phase space is it what is it well okay so my claim is the correct way to think about coarse graining is it has to be a computationally feasible thing to do so you can make all kinds of elaborate measurements on these molecules but it has to be a limited amount of computation that you're doing in trying to invert the dynamics and so on and so then the the basic point is that computationally reversed irreducibility implies that even when you start from a simple to describe initial condition it is inevitable that you effectively encrypt that initial condition to the point where a an observer with bounded computational ability can't decode it and work it at work out where it came from so put another way when we see he which is kind of the the the sort of the high entropy the disordered version of energy when we see heat if we had a sufficiently sophisticated computational system we could invert the motions of all those molecules and we could say oh that piece of heat came from this very simple initial condition but in practice we can't do that so the the presence of sort of heat is a consequence of something that we consider to be completely disordered energy is a consequence of the fact that our measurement process is only of sort of isn't computationally sophisticated enough to invert the the dynamics that led to the disorder that we see there there's a there's a fine description I think of this in a section of my new kind of science book the beginning of chapter 9 the end of chapter 9 is about the kind of fundamental physics that we're talking about here the beginning of chapter 9 is about 2nd or thermodynamics and you guys are really encouraging me because I put those together in the same chapter because I thought they were conceptually related and I really had thought people had completely forgotten that conceptual relation by the way this argument for the second law is critical in our theory of fundamental physics because we need this kind of microscopic randomness to be able to explain how continuum behavior occurs and to be able to do things like explain why one isn't getting Manhattan distance on you know in in these some and having pure so grid-like structures in space-time okay oh boy we have a lot of questions here all right let's let's see if we can zip through these um okay there's a practicer van der that probably is something in Latin which I can't translate immediately but Tim would like a general discussion of different digital physics approaches and how these new theories approach things differently and handle the usual criticisms about discrete versus continuous which have already been discussed so I think a lot of sort of what one means by digital physics has really revolved around cellular automata I've been a huge enthusiast of cellular automata a lot of stuff I figured out has been a consequence of looking at cellular automata I had always felt that cellular automata were a singularly bad model of fundamental physics I mean ironically enough when I first started working on cellular automata I originally invented my version of cellular automata before I knew that people had studied them in different forms before as a result of trying to idealize two phenomena one was self-gravitating gases and the other was neural networks this was around 1980 or so and ironically enough cellular automata are good models for many things but they're uniquely bad models of both self-gravitating gases which have long-range forces in them and neural networks which have sort of long-range connections in them but I also think that cellular automata are not good models for for fundamental physics I think that they their notion of this sort of rigid notion of space and time is just not a good fit with with what we kind of with sort of having the flexibility to have sort of emergence based in time which is what we've discovered is what leads to things like general activities special relativity quantum mechanics and so on now having said that cellular automata are a fantastic source of intuition and you know that's where the intuition that led me to start studying the kinds of models we're talking about here all came from cellular automata it's just I wasn't looking specifically at cellular automata in in trying to understand what might be underneath space and time and I think the questions like how do you get rotational invariance in a cellular automaton you can get some I got examples of that a new kind of science but it's kind of a mess and it's very unnatural whereas in these models where there's sort of a just connectivity data where you're building your own space rather than having space imposed upon you those things are much more natural and I'm actually a little I haven't heard from my friend Edie fredkin who's been a big big proponent of digital physics I sent him the stuff I am and concern didn't hear from him yet but oh maybe it's in my email right now um okay does this theory disallow the exponential speedups proposed by Shor's algorithm interesting question interesting question so well I'll take one crack at this that to make the statement that causal and variance so Jonathan already mentioned this point about Turing machines non-deterministic Turing machines and quantum Turing machines and this sort of the the the picture that shows algorithm for factoring on a quantum computer the sort of picture is oh it trees out all the possibilities in parallel and then just tells you the answer the real story I think well two points first of all back in what was it 1981 to something around that time I I worked on quantum computers long before anybody heard of quantum computers actually dick Feynman and I tried to work together on studying quantum computers we had somewhat incompatible approaches to to science his was much more let's go calculus piece of paper mine was much more go go run a computer simulation I don't think either of us necessarily believed what each other was getting but it was setting that aside the thing that we both thought was a big issue was this question of when you've done the computation how do you do the measurement and would you end up in a situation where you were so you know you had so much sort of detail to untangle in the measurement that you wouldn't actually gain a thing and the paralyzation in quantum in the in the quantum mechanics so now in terms of these models where we actually have this picture of the multi-way system is the whole story and then we're sort of having to read out pieces of a multi-way system this question of what exactly is involved in measurement I think comes more to the fore and I think this question of what we can do in the in the in the light of causal invariance how much Treeing out can we really do is interesting and I think Jonathan has thought more about this so maybe he can make some comments about this sure I mean Stevens Stevens points already covers the majority of what I was what I was going to say so so yeah I mean there's this problem of there's basically a trade-off here between the more Treeing out you get in the multi way evolution the more complicated your procedure has to be in order to be able to collapse that multi way evolution back down to a single evolution thread so that you can guess effectively a classical answer out which is what you have to be able to do if you want to be able to you know factor an integer or something because you know in ordinary quantum computers you set this up so that the the eigenstates that give you the wrong factorization have amplitudes that exactly cancel so that in the end the eigenstate that gave you the correct factorization is the only one you see we have the same problem so we have to we have to do this this completion procedure on them on the multi way evolution graph that collapses all these branches down to give you a single causal and variant result and the more exponential Treeing out there is the more complex that the more sort of more computationally irreducible I should say the that completion procedure is going to be and so eventually there's a kind of point where the the benefit these curves basically cross over there's a point where the benefit of the exponential Treeing out intersects with sort of the loss that you're getting from this exponentially this completion procedure that's sort of exponentially increasing computational complexity and this puts bound we don't know it we don't know definitively that it rules out the potentially exponential speed ups of Shor's algorithm but it certainly puts bounds on the speed ups or things like shores algorithms this is related to the thing I was mentioning earlier about the bounds of how much the complexity classes of P versus V Q P can be related that's something we still have to compute in detail but this is as far as I know you know from from having looked at this with quantum computing literature on this kind of thing this is the first kind of definitive bound that's kind of based on a a well-defined interpretation of quantum mechanics that the puts well-defined bounds on on sort of the potential speed up for things like Shor's algorithm I think the main point here is that you know gosh I've been sort of waiting for this for 40 years is is that making the measurement process more realistic is what you need to do to know exactly what you can really get out from a quantum computer and I've been I've been sort of saying this vaguely for 40 years but I think we now have an actual way to do this and I think this is something we need to do or somebody else needs to do it's somebody to actually work out you know what is the cost of measurement so to speak which I don't think we really have understood very well before but now we have a pretty concrete way of assessing the cost of measurement and so that should be done okay let's see um is it possible to render a perspective projection from within the graph by tracing geodesics over the graph for example to a sphere with a radius centered on the same node so that's an interesting idea so that's that's an idea for visualization of these graphs that is an interesting idea so I mean in other words to look the geodesic eyes view of the graph we haven't done that I mean it's good idea we could try it I mean it's so you can try it I mean I think that that when we start thinking about you know what does the what does the what does the electron see when it's propagating through space that's kind of what we're going to have to look at um and and particularly when we're looking at multiple steps and the evolution of the graph combined with the motion of the electron and so on that will be an interesting thing to do good idea not thought of that okay Gabriel Lewin burger why are you not using pure lambda calculus which is the simplest model and as confluent um okay well let's see I did discuss that actually a little bit in section 7 of my technical introduction let me um what's the best way to say this because what really matters here is kind of the pattern matching side of things and the fact that we have essentially this data structure that's representing the hyper graph that we think is representing space and we're operating on that hyper graph and pure lambdas are kind of a let's just eat function arguments you know as they come to us sort of one at a time so to speak rather than let's bite into this actual sort of structure that is the hypergraph and do things to that structure I think it's probably my best um I I certainly thought about this question of whether we could somehow use think about this as pure lambdas and I don't think it really makes sense because I think the pure lambdas are really that they actually another way to think about it I mean pure lambdas tend to you know they eat one piece of food at a time so to speak they're they're just going along you know and particularly if you've curried things you've gosh that's a that's a terrible food analogy right there but um the you've um you're just feeding to the lambda another another expression another expression another expression that's different from taking them out of a hypergraph to do things with them um okay Omar here okay this is that this is directed you Jonathan which is good how about the holographic principle any evidence from these multi wave processes of why quantum gravity could be described by a lower dimensional quantum field theory great he's is telling that to you so go okay yeah perfect so okay what one sort of general point to make about these these questions about connections to other theories we've actually answered a bunch of these Stephan and I of Furby for the bull from physics websites if you go to the woman physics Q a part of the website that there's a whole section about relations other theories and a lot of the ones that have come up like Luke bond and gravity like things like the holographic principle we have at least sort of shortish answers to those questions which we'll know those will no doubt changes our understanding of bulbs but at least at our present level of understanding we have some some answers there so let me give a quick summary of how this relates to the holographic principle and in particular to this idea of a DSC of T correspondence which is kind of the most concrete formulation formulation of the holographic principle that we currently have which is what emerges from string theory so the basic idea with a DSC ft correspondence is ad s that has anti-de sitter so gravitation of bulk gravitational theory in anti-de sitter space in in some d dimension some some d dimensional ad s can be described effectively in terms of a conformal field theory defined on a d minus 1 dimensional boundary to that book the ball KD s region and this is a sort of somewhat bizarre kind of intuition breaking resultant or physics but actually it's a very natural consequence of our models and at least in toy can get sort of mini holographic principles appearing in our multi-bit causal graphs let me give a brief summary sketch of how this works and you can go see the Q&A so up for probably a better description so if you consider this fundamental structure this multi way causal graph well as I as I mentioned earlier you basically have you have causal or your directed edges represent causal connections between updating events not only on the same branch of history as in the standard space-time calls autographs but actually between different diff different branches of history right and the kind of the general intuitive claim is all the stuff we talked about to do with relativity that's to do with space-time causal graphs and therefore those all concern the causal edges that connect events on the same on a single branch of history all the quantum results we've talked about with multi way evolution effectively concerned these different branches of histories they're about the causal edges that connect these different branches of history so now here's the point now imagine you all you take one of these bundles of calls alleges that corresponds to a particular multi revolution branch and you draw effectively a wall around it so now what you have are brought our causal edges between different branches of evolution history flux being flux through this wall and those are described by something like a conformal field theory on the boundary but inside you have a single multi way evolution branch which is therefore a spacetime causal graph described by general relativity so you immediately have this notion of eight of a bulk 80s sort of gravitation theory inside this multi-way evolution branch being described in terms of fluxes of course Ledger's which we can think of in terms of conformal field theories through the through the bounce through the through the d- one-dimensional boundary and there are more precise versions of this I I give some details in my quantum mechanics paper about how this relates to things like the black hole information paradox and relations between sort of beckon Hawking entropy and entanglement entropy and other kinds of predictions that have been made from the holographic principle but the sort of the TLDR version is the holographic principle is a very very natural statement within our models basically because of structure of the multi way causal craft I'd say there's a point about where people can send papers and so on yeah I mean people people who are like you know researching these various things like the holographic principle and so on who we'd love to hear from you and there are lots of lots of interesting relations to what we're doing that I think can be explored um okay so Eric 4G is saying please look at his 2002 dissertation about differential geometry in computation electrum and another one 2004 about discrete differential geometry on causal graphs okay that sounds that that title at least sounds highly relevant so yes will will if you if you send mail on our website there's a Contact information link and there's if you if you send mail there that will that's sort of the the easiest way to communicate um ah okay there's a question here who cares about peer review oh don't get me started on that whole question I you know a sad fact I I haven't written you know this this I just sent in to archive the the 450 page technical introduction to this project that I wrote um and that is the first academic style paper that I've written since 1986 and I was I realized I pull Ginsberg who started the archive preprint server has been a friend of mine for a long time and I had been asking Paul about how do I submit this paper and he sent me back mail over last weekend saying a hundred thousand people have succeeded in submitting papers to our Co you know and they gave me some details about what to do so so um it was it's it's kind of from you know sadly when I when I did physics for living so to speak one of my heuristics was any truly sort of original idea could not get through peer review only incremental progress on things that already existed could but um that that's that's a that's a perhaps overly cynical point of view but Tim it's some yeah let me not get started on that that's that that's a sociology of science issue which um which is probably not not pertinent to this okay somebody is asking did we solve the homework problem from the previous livestream does your theory have a maximum temperature so we did talk about that and actually I'm now trying to remember that the main conclusion was yes there's a maximum temperature and the argument was pretty nice and I'm actually forgetting it offhand Jonathan do you remember that argument yeah yeah so so basically how this works is or how this might work is the okay obviously temperature is some measure of average kinetic energy it's sort of over over some region of space and we have an immediate proxy for that in our causal graph because we have this notion of momentum that Stephen was talking about earlier so we have this notion that momentum is flux of causal edges through sort of vertical time like hyper surfaces in the causal graph so basically the notion of the question of is there an average temperature can really be recast in terms of is there an average flux density for causal edges beyond which you know the causal graph kind of falls apart or something and actually the answer seems to be probably yes because if you have a flux density of causal edges through a time like hyper surface that's too high it will basically it will it will cause that region of the causal graph to become causally disconnected for essentially the same reason as it doesn't if you try and form a black hole by compressing too much matter in the same region of space you get some temperature theoretic analog of a Schwarzschild radius where so you know if you try and compress too much energy into a region of space that's again you're getting too much flux density of course ledges just through a space like hyper surface rather than through a time like one and so we so we have exactly the same thing basically the phenomenon of the this principle says if you try and heat up a region of space beyond a certain temperature it will inevitably collapse to something to something analogous to a black hole and the causal graph will become disconnected we haven't actually computed exactly what that is it's it's a very very high temperature I suspect it'll probably be something of the order of the Planck temperature because that's kind of the continuum analog of the same sort of phenomenon but but the other the short answer is yes there is some notion of a maximum temperature in our model right but so why is it not the case that just in traditional general activity that you know there's a you know when you have a certain amount of of heat that corresponds to a certain team you knew and that you know in if you have that amount of heat in some region that's going to end up being a I mean just like in the traditional black hole setup you should be able to get that same you know you should in in in continuum theories you should get gravitational collapse if you have so actually I don't even know but that in in sort of standard bekenstein Hawking type thinking is there a maximum temperature there there should be yeah there is there is one that that's that there is this notion of the planck temperature so this is so the planck temperature is this is this fundamental derivative it's a composition of the of G H bar C and all these other units and effect it you know one way you can think about that dimensional analysis is that it's the it's the temperature beyond which that region of space will effectively be contained within its trust child radius right so the question is really so I suspect will end up with the same kind of maximum temperature although we might have some other interesting effects because because of this question that's more like the so called hagedorn temperature which came up in particle physics where you're just generating more and more different kinds of particles as you put more energy into into a particular region and that that's that's an interesting question which depends on the spectrum and particles which we don't know yet okay um like a for us here is eternal recurrence at different space timescales and inevitable conclusion of your theory I don't think so I mean that would be some kind of fractal nested version of space-time and I don't think we have that I don't think the yeah I don't think there's a scale interesting question whether there are to what extent there's scale invariance I mean there is there is some effective field theory some renormalization group sort of story about looking at effective looking at the variation of the effective evolution rule on different scales but I don't think that any in any direct way that there's a sort of recurrence of that type um okay Hugo Lina is asking in the blog article you add the causal dependencies to the a BBB graph can you walk through a few of those dependencies to clarify their meaning okay let's take a look at that by the way Stephen just one thing a bunch of people are telling me that we need to transition to the philosophy stream very well okay all right okay okay okay well then okay all right well we've got so many interesting questions here all right so so we'll have to pick that up another time I'm sorry well actually be really good let's just since somebody is trying to read something in detail let's just very quickly try and go through that or maybe we can take that offline and somebody can can explain that we should be able to really go through that in detail um all right well listen this is great guys and much appreciated and you know we'll do a round two it's yeah um that's good all right so for people who are interested we will be transitioning a totally different kind of strand of things talking about the philosophy of the implications of these things for philosophy and before that I need a bite to eat so see you guys soon thanks for joining us okay bye

Channel: Wolfram

Views: 14,865

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: vVsb8E33Nbw

Length: 124min 16sec (7456 seconds)

Published: Wed Apr 15 2020