The rule defines how to take two connections in the hypergraph (which in this case is actually just a graph) and transform them into four new connections, creating a new element in the process. There’s quite a bit of mathematical sophistication involved (for example, we have to consider curvature in space+time, not just space), but the bottom line is that, yes, in various limits, and subject to various assumptions, our models do indeed reproduce Einstein’s equations. Or could it be that this is a kind of question that’s just outside the realm of science? But in the end we can generate a series of fits for the effective dimension—and in this case these say that the effective dimension is about 2.7: it’s limiting to dimension 2, as it should: What does the fractional dimension mean? And they don’t have any way to know how the causal graph was drawn. Anyway, congratulations for discovering new ways to fascinate humans! So much Time AND effort finally paid off !!!! So this gives us a way to measure the effective dimension of our hypergraphs. At least, looking at the quality of the stuff on this page, it looks like Wolfram has solved it at last, after many many decades of work. Events happening on one side can’t influence ones on the other, and so on. Here’s an example of a wonderful correspondence: curvature in physical space is like the uncertainty principle of quantum mechanics. In terms of graph, can two points be connected with something different than a line? And a crucial idea in our model is in a sense just to do all of them. Authors: Stephen Wolfram. For me, one of the most satisfying aspects of our discoveries over the past couple of months has been the extent to which they end up resonating with a huge range of existing—sometimes so far seemingly “just mathematical”—directions that have been taken in physics in recent years. General relativity’s description of curvature in space turns out to all be based on the Ricci scalar curvature R that we encountered above (as well as the slightly more sophisticated Ricci tensor). It’s a remarkable conceptual unification. On the next step, though, all that can be done is to replace the A—in both cases giving BBBB. Normally the area of a circle is πr2. Where we go from there..! But actually the multiway graph gives us that. It isn’t surprising that after thousands of years, we still haven’t perfected the seer’s skill set. In talking about quantum mechanics, other frames are useful. So are there situations in which the two kinds of phenomena can mix? The particles are all effectively “little lumps of space” that have various special properties. I’ve always assumed that any entity that exists in our universe must at least “experience the same physics as us”. Why is it called what it’s called? For example, there are closed timelike curves, sometimes viewed as allowing time travel. It’s not that we have virtual particles “in space”, that are having an effect on space. But that’s not what the universe does. Something could also be represented by multiple values. But remember, the pictures we’re drawing are just visualizations; the underlying structure is a bunch of discrete relations defining a hypergraph—with no information about coordinates, or geometry, or even topology. And that choice of foliation corresponds to a description language which gives us our particular way of describing the universe. But even though the structure is well represented in the Wolfram Language, the “use case” of “running the universe” is different from what the Wolfram Language is normally set up to do. The w that appears there is a new element that’s being created, and the only requirement is that it’s distinct from all other elements. Essentially what’s happening is that there are always pairs of particles and antiparticles being created, that annihilate quickly, but that in aggregate contribute a huge effective energy density. But in our models we don’t start from anything like this, and in fact space and time are not even at all the same kind of thing. Or, said differently, all the observer can ever observe is the network of causal relationships between events—or the causal graph that we’ve been talking about. Very interesting! The universe is effectively using all possible rules. But there is a subtlety in exactly how this works that might at first seem like a detail, but that actually turns out to be huge, and in fact turns out to be the key to both relativity and quantum mechanics. There’s a fundamental feature of our causal graphs that we haven’t mentioned yet—that’s related to information propagation. Inevitably there is a great computational distance between the underlying rule and features of the universe that we’re used to describing. And I have to say that our recent success in getting conclusions just from the general structure of our models makes me much more optimistic about this possibility. And typically it won’t even be finite-dimensional. If you’re an observer far from a black hole, then you’ll never actually see anything fall into the black hole in finite time (that’s why black holes are called “frozen stars” in Russian). ... How We Got Here: The Backstory of the Wolfram Physics Project April 14, 2020. [4][8] The Wolfram model is said to reproduce key features of both quantum mechanics[9] as well as special and general relativity. Here are the graphs we get by doing this for successive slices: We call these branchial graphs. Our usual impression of the world is that definite things happen. The version of time in our models is in a sense very computational. If we based everything on the traditional methodology of mathematics, we would in effect only be able to explore what we somehow already understood. So how is the effort to try to find a fundamental theory of physics going to work in practice? Of course, as with physical experiments, it matters how we define and think about our experiments, and in effect what description language we use. But sometime—I hope soon—there might just be a rule entered in the Registry that has all the right properties, and that we’ll slowly discover that, yes, this is it—our universe finally decoded. We plan to have a centralized effort that will push forward with the project using essentially the same R&D methods that we’ve developed at Wolfram Research over the past three decades, and that have successfully brought us so much technology—not to mention what exists of this project so far. They have to have a foliation where successive time slices just pile up, and never enter the disconnected pieces. A visual summary of Wolfram's theory. The speed of light c in our toy system is defined by the maximum rate at which information can propagate, which is determined by the rule, and in the case of this rule is one character per step. Normally in physics one puts in relativity by the way one sets up the mathematical structure of spacetime. And in the past it’s often been a struggle to reconcile them. Thank you so much for making this discovery “accessible” to us all. And in fact, not only can we identify light cones in our causal graph: in some sense we can think of our whole causal graph as just being a large number of “elementary light cones” all knitted together. There’s a footnote here. The Wolfram Physics Project is a project launched by computer scientist and physicist Stephen Wolfram to find the fundamental theory of physics. Doing new measurements is equivalent to getting entangled with new quantum states—or to moving in branchial space. Let’s go back to what we discussed when we first started talking about time. And perhaps it will take more ideas before we can finish the job of finding a way to represent a rule for fundamental physics. The uncertainty principle says that if you measure, say, the position of something, then its momentum, you’ll get a different answer than if you do it in the opposite order. Not only can the causal graph split; the spatial hypergraph can actually throw off disconnected pieces—each of which in effect forms a whole “separate universe”: By the way, it’s interesting to look at what happens to the foliations observers make when there’s an event horizon. The full story—going back to Stephen’s early life as a physicist—is in Stephen Wolfram’s post, Read more But at that point we were just talking about “empty space”. [10][13], While Stephen Wolfram claims the project has been a success with scientists and others engaging with the project through the livestreamed content,[14] other prominent physicists have leveled criticism at the project. Let’s look at a particular, simple rule from our infinite collection: {{x, y, y}, {z, x, u}} → {{y, v, y}, {y, z, v}, {u, v, v}}. And with this elementary length, the radius of the electron might be 10–81 meters. If the universe is processing every conceivable rule, then a subset of it can encompass any kind of computable universe within itself (including copies), just as a universal Turing machine can emulate any other type of computer. Quantum measurement is really about what an observer perceives. It’s basically making us a very simple “piece of space”. In 2012, he was named an inaugural fellow of the American Mathematical Society. But what does moving in rulial space correspond to? Categories of articles by Stephen Wolfram. And we can imagine that as our system evolves, we’ll get larger and larger branchial graphs, until eventually, just like for our original hypergraphs, we can think of these graphs as limiting to something like a continuous space. Scientist Stephen Wolfram opens up his ongoing Wolfram Physics Project to a global effort. Enter Stephen Wolfram. Stephen Wolfram Invites You to Solve Physics. The project was launched in April 2020 with the main contributors being Stephen Wolfram, Jonathan Gorard and Max Piskunov. When he introduced “rulial space” that issue went away and I was sold. Assuming we’ve drawn our causal network so that events are somehow laid out in space across the page, then the light cone will show how information (as transmitted by light) can spread in space with time. But let’s look more closely at our light cones. In what we’ve discussed so far we’re imagining that there’s a particular, single rule for our universe, that gets applied over and over again, effectively in all possible ways. Very captivating reading, an amazing project, and thank you for the opportunity to see its development in real time. Here is the graph after one more update, now no longer trying to show a progression down the page: So how does this relate to time? In other words, from the property of causal invariance, we’re able to derive relativity. (By the way, there’ll be an analog of curvature and Einstein’s equations in rulial space too—and it probably corresponds to a geometrization of computational complexity theory and questions like P?=NP.). But actually there’s something I call the Principle of Computational Equivalence, which says that almost any time the behavior of a system isn’t obviously simple, it’s computationally as sophisticated as anything. It’s something that (at least so far) is only clear in the context of our models. (It isn’t terribly surprising that a fundamental theory of physics—inevitably built on very abstract ideas—is somewhat complicated to explain, but so it goes. Just wanted to leave my footprint. Nothing is something, and therefore apart of everything, but if everything is, than nothing can’t be, if nothing is not, than neither is everything, which means that if everything is not, than nothing is. Or you could multiply the terms first. And if this happens fast enough, we’d never be able to “see the discreteness”—because every time we tried to measure it, the universe would effectively have subdivided before we got the result. But in our model, it’s not just a definition, and in fact we can successfully derive it. But branchial space is something more abstract—and much wilder. Or, in other words, there’s a maximum rate at which we can entangle with new quantum states. So far as I understand from human history, any new way of looking at things ( even if ill-considered by the establishment at first) has led to better and further understanding of our world. And there’s one very important thing about it: it’s basically guaranteed to have causal invariance (basically because if there’s a rule that does something, there’s always another rule somewhere that can undo it). In the end, if we’re going to have a complete fundamental theory of physics, we’re going to have to find the specific rule for our universe. Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist who is the founder and CEO of Wolfram Research, a company behind So within that hypergraph, is there a way to identify things that are familiar from current physics, like mass, or energy? And if their energies end up being low enough, they’d basically collect in gravity wells around the universe—which means in and around galaxies. And there is difficult work to do on both sides. We’ve got physical space, branchial space, and now also what we can call rulial space (or just rule space). To an observer far from the black hole, it’ll seem to take an infinite time for anything to fall into the black hole. And it looks like these causal edges have an important interpretation: they are associated with mass (or, more specifically, rest mass). Just like there’s a maximum speed in physical space (the speed of lightc), and a maximum speed in branchial space (the maximum entanglement speed ζ), so also there must be a maximum speed in rulial space, which we can call ρ—that’s effectively another fundamental constant of nature. Think about expanding out an algebraic expression, like (x + (1 + x)2)(x + 2)2. We think we’re “going forward in time”. And if you trace through the picture above you’ll find out that’s what always happens with this rule: every pair of branches that is produced always merges, in this case after just one more step. How does this all relate to the detailed standard formalism of quantum mechanics? So how do things like that work in our models? And it’s much more wonderful, and beautiful, than I’d ever imagined. We can represent this with a graph that shows all possible paths: For the very first update, there are two possibilities. But here I’m going to give a fairly non-technical summary of some of the high points. A few months ago I would also have said that I don’t even know if we’ve got the right framework for finding it. We don’t (yet) know an actual rule that represents our universe—and it’s almost certainly not the one we just talked about. But in our models it just comes directly from the analogy between branchial and physical space. In the case of physical space, we argued (roughly) that the presence of excess causal edges—corresponding to energy—would lead to what amounts to curvature in the spatial hypergraph, as described by Einstein’s equations. But in the early 1980s, when I started studying the computational universe of simple programs I made what was for me a very surprising and important discovery: that even when the underlying rules for a system are extremely simple, the behavior of the system as a whole can be essentially arbitrarily rich and complex. This theory it’s so amazing. I’m frankly amazed at how much we’ve been able to figure out just from the general structure of our models. Congratulations. It’s a phenomenon that’s implied by the add-ons to the standard formalism of quantum mechanics that describe measurement. But why should that be true? Or, said another way, in the effort to sample space faster, our observer experiences slower updating of the system in time. And we see it’s just a grid: Here are three other possible sequences of updates: But now we see causal invariance in action: even though different updates occur at different times, the graph of causal relationships between updating events is always the same. You could expand one of the powers first, then multiply things out. Please enter your comment (at least 5 characters). And this is basically how I think space in the universe works. Well, consider fractals, which our rules can easily make: {{x, y, z}} → {{x, u, w}, {y, v, u}, {z, w, v}}. So you have a follower in me, jajaja. At the lowest level, the rules we’ve got are about as minimal as anything could be. This is again somewhat complicated. But as entities embedded in the universe, we’re picking a particular foliation (or sequence of reference frames) to make sense of what’s happening. For example, we might wonder what the “zero of energy” is. Recall our discussion of causal graphs in the context of relativity above. It looks it’s “trying to make” something 3D. And I’ve never seen anything that comes close. I was personally struggling with “rules” as the fundamental way the universe works. If there are always all these different possible paths of history, how is it that we ever think that definite things happen in the world? This kind of balance between branching and merging is a phenomenon I call “causal invariance”. But what’s important is that it’s realistic that they can; there’s a lot one can understand before one hits computational irreducibility. It’d be as if the speed of light is infinite. But what is that space? There is also a whole host of subtle mathematical limits to take. The answer it seems is that all three share the same underlying computational architecture. Nothing could be farther from the truth. But if we look at a particular slice in one of these foliations, what does it represent? In general, the “volume” of the d-dimensional analog of a sphere is a constant multiplied by rd. If we keep on going longer and longer it’ll make a finer and finer mesh, to the point where what we have is almost indistinguishable from a piece of a continuous plane. But regardless of how this kind of expansion works in our universe today, it’s clear that if the universe started with a single self-loop, it had to do a lot of expanding, at least early on. The foliation has got a bunch of states in it. We might have a collection of relations like. And given this finite “speed of emulation” there are “emulation cones” that are the analog of light cones, and that define how far one can get in rulial space in a certain amount of time. And what this means is that in the rule-space multiway graph, we can expect to make different foliations, but have them all give consistent results. Calculus has been built to work in ordinary continuous spaces (manifolds that locally approximate Euclidean space). It has to be a language that humans can understand. We’ll be running a variety of educational programs. A spacelike direction is one that involves just moving in space—and it’s a direction where one can always reverse and go back. And here there’s an interesting possibility that’s relevant for understanding cosmology. But the point is that we’ve basically already defined at least some elements of our description language: they are the kinds of things our senses detect, our measuring devices measure, and our existing physics describes. But the basic point is that both theories are consequences of causal invariance—just applied in different situations. Like that the whole hypergraph for the universe is always expanding, but pieces are continually “breaking off”, effectively forming black holes of different sizes, and allowing the “main component” of the universe to vary in size. And again, it’s quite wonderful: at least in some sense, the answer is that it’s the path integral—the fundamental mathematical construct of modern quantum mechanics and quantum field theory. Thank you for your service and work. We started seeing some deep structural connections between relativity and quantum mechanics. We’ll discuss how this relates to quantum mechanics in our models later. While we have an excellent theory of how gravity works for large objects, such as stars and planets and even people, we don’t understand gravity at extr… [5] In a controversial move, Wolfram did not seek peer review prior to publishing his work. OK, so what about branchial space? Note: From 1987 to 2020, Stephen Wolfram’s intellectual efforts have not primarily been reported in academic articles. For example, let’s imagine we try to make a foliation in which we freeze time somewhere in rulial space. Many of the computational phenomena obtained in these systems bear analogy to Wolfram's previous investigations into cellular automata. That something similar is the multiway causal graph: a graph that represents causal relationships between all events that can happen anywhere in a multiway system. What this rule says is to pick up two relations—from anywhere in the collection—and see if the elements in them match the pattern {{x,y},{x,z}} (or, in the Wolfram Language, {{x_,y_},{x_,z_}}), where the two x’s can be anything, but both have to be the same, and the y and z can be anything. But then there’ll be lots of causal edges associated with the particle, defining its particular energy and momentum. We just apply a simple rule to them, over and over again. A book, A Project to Find the Fundamental Theory of Physics, was published about the project in June 20… But actually—as I first discovered in the early 1980s—this kind of intrinsic, spontaneous generation of complexity turns out to be completely ubiquitous among simple rules and simple programs. Because there’s no way to tip the foliation at more than 45° in our picture, and still maintain the causal relationships implied by the causal graph. Maybe one day we will have built up familiar ways of talking about the concepts that are involved. And that’s how a region of the universe can “causally break off” to form something like a black hole. We do know that whenever there’s computational irreducibility in a system, there are also an infinite number of pockets of computational reducibility. It’s not what our ordinary intuition tells us should happen. This is very interesting. (On the surface of the Earth, imagine a circle drawn around the North Pole; once it gets to the equator, it can never get any bigger.). Stephen Wolfram shares his 40-year research journey that has culminated in the Wolfram Physics Project, plus history and developments on the search for the fundamental theory of physics. But at least in the way I have done it, the essence of language design is to try to find the purest primitives that can be expressed this way. But now I realize that this isn’t true. Here’s the multiway system for the sorting process annotated with all causal relationships for all paths: And, yes, it’s a mess. And I have to say that I don’t think our recent discoveries shed any particular light on this—because they basically say that lots of things in physics are generic, and independent of the specifics of the underlying rule, however simple or complex it may be. But one of the beautiful outcomes of our project so far has been the realization that at some deep level general relativity and quantum mechanics are actually the same idea. (Notice that in a finite universe, there are only ever finitely many rules that can ever apply.). And let’s try to make this the time in human history when we finally figure out how this universe of ours works! And that means there’s ultimately a lot more we can say about it. (Its most common name is “confluence”, though there are some technical differences between this and what I call causal invariance.). (There could still be other universes that do various levels of hypercomputation.). Here are examples for graphs corresponding to 2D and 3D lattices: And if you now count the number of points reached by going “graph distance r” (i.e. OK, so how does this work? If we look at the causal graph, we’ll see that you can effectively “go everywhere in space”, or affect every event, very quickly. It is incredible that you have found a way to unify relativity and quantum mechanics, absorb a lot of the newer attempts to reconcile these and make testable predictions! [15], Wolfram's decision not to seek traditional peer-review was also a point of contention in the physics community. We didn’t put in anything about this shape. It almost seems like everyone has been right all along, and it just takes adding a new substrate to see how it all fits together. One thing is that it has implications for geodesics. Stephen Wolfram, the famed physicist and computer scientist known for his company Wolfram Research, believes he's close to figuring out the fundamental theory of physics. [7], The project is built around exploring simple computational systems that create complex networks of causal relationships. Maybe even lots of different kinds of oligons: a whole shadow physics of much lighter particles. For now, this is just a phenomenon associated with the structure of space. What needs to be true for us to have d-dimensional space, as opposed to something much wilder? You’ll get some kind of cone (here just in 2D): The cone is more complicated in a more complicated causal graph. It’s that the same stuff that corresponds to the virtual particles is actually “making the space”, and maintaining its structure. The “causal edges” are the causal connections between events, shown in the picture as lines joining the events. You just need to toy with it and your imagination long enough! For example, everything, nothing, and something. So—along with the two young physicists who’d encouraged me—I began in earnest in October 2019. And this is particularly common with the very structureless models we’re using here. The foliation we had above is relevant to observers who are somehow “stationary with respect to the universe” (the “cosmological rest frame”). Or, put another way, just how simple is the rule for our universe going to end up being? And this independence of orders is essentially causal invariance. What would happen to your models if you applied mathematical constructs to philosophical concepts. This approach has the same ideas that I realized when I tried to figure what the time and space really is. I expected that we’d start exploring simple rules and gradually, if we were lucky, we’d get hints here or there about connections to physics. So it came as a big surprise when we recently realized that actually in our model, there is something we can point to, and say “that’s energy!”, independent of what it’s the energy of. But when we think about how “space is maintained” it’s basically through all sorts of seemingly random updating events in the hypergraph. OK, so how does it all work? There are very different things that can happen in our models: In the first example here, different parts of space effectively separate into non-communicating “black hole” tree branches. Is casual invariance just associativity? But the surprising thing is that there’s a remarkable depth of richness before one hits irreducibility. In other words, to keep time frozen, more and more quantum states have to be pulled into the “reality distortion field”, and so there’s less and less coherence in the system. OK, things are getting fairly complicated here. And we can translate this into saying that we imagine a series of “moments” in time, where things happen “simultaneously” across the universe—at least with some convention for defining what we mean by simultaneously. In our model, everything in the universe—space, matter, whatever—is supposed to be represented by features of our evolving hypergraph. And I don’t know how hard that’s going to be. If we generalize to d dimensions, it turns out the formula for the growth rate of the volume is , where R is a mathematical object known as the Ricci scalar curvature. The Wolfram Physics Project Hopes to Find Fundamental Theory of Physics. through spacelike hypersurfaces) or in space (i.e. We can mark spacelike () and timelike () hypersurfaces in the causal graph for our toy model: (They might be called “surfaces”, except that “surfaces” are usually thought of as 2-dimensional, and our 3-space + 1-time dimensional universe, these foliation slices are 3-dimensional: hence the term “hypersurfaces”.). If you know about special relativity, you’ll recognize a lot of this. By the way, it’s worth mentioning what a “flux of causal edges” corresponds to. It’s a strange but rather appealing picture. The answer in our setup is basically no. But let me try to give a flavor of it. But to get to the point where we can understand the elegant bigger picture we need to go through some detailed things. (It might approximate a projective Hilbert space.) It’s all related relative abstract mathematics depending upon one’s perception! (There’s some more detail in my technical document; Jonathan Gorard has given even more.). One of the big predictions of general relativity is the existence of black holes. But as we’ve gotten further in investigating our models something amazing has happened: we’ve found that not just one, but many of the popular theoretical frameworks that have been pursued in physics in the past few decades are actually directly relevant to our models. Its 3m in the morning, and i can’t pull myself away from this website. One of the great achievements of the mathematical sciences, starting about three centuries ago, has been delivering equations and formulas that basically tell you how a system will behave without you having to trace each step in what the system does. But on the other hand, one feels calmer than at least having an idea of how the crazy quantum world works, details are missing but it is already a start. In the path integral there’s a quantity called the action—which is a kind of relativistic analog of energy—and when one works things out more carefully, our fluxes of causal edges correspond to the action, but are also exactly what determine the rate of turning of geodesics. We drew foliations and said that if we looked at a particular slice, it would tell us the arrangement of the system in space at what we consider to be a particular time. In a sense computational irreducibility implies that there will always be surprises, and that’s certainly what I constantly find in practice, not least in this project. [12] Stephen Wolfram and Jonathan Gorard have posted preprints on the topic to the arXiv; Gorard's was submitted to the journal Complex Systems, which was founded by Wolfram in 1987. , like mass, or the events that define the branchial graph been... Beyond all or inklings of understanding and bring unfathomable capabilities let me to! 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