It already seems impressive that hints at derivability of some fundamental “Laws” of Physics have been obtained in a few months of work by a small ( even if talented) team. But if one wants to “really understand what’s going on” in quantum mechanics, it’s something that definitely does matter. But so if we want to find out if our models are reproducing Einstein’s equations for gravity, we basically have to find out if the Ricci curvatures that arise from our hypergraphs are the same as the theory implies. 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. Needless to say, of course, our modern computational paradigm did not exist a century ago when “spacetime” was introduced, and perhaps if it had, the history of physics might have been very different. But in our models there’s in a sense too much emergence for this to work. The Wolfram Physics Project is a project launched by computer scientist and physicist Stephen Wolfram to find the fundamental theory of physics. This read sent all kinds of chills down my spine Thank you for sharing. What is “inside” these steps? 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. This is so interesting and exiting to get a glimpse of what space and time is. If space is effectively d-dimensional, then to a first approximation this volume will grow like . But like in the spatial case, there’s a correction term, this time proportional to the so-called Ricci tensor . But I never got anywhere. But what certainly helps me, at least, is that I’ve now been doing computer experiments for more than forty years, and over that time I’ve been able to slowly refine the art and science of how best to do them. Then for each of the results of these, there are four additional possibilities. And this is particularly common with the very structureless models we’re using here. In the effort to serve what people normally want, the Wolfram Language is primarily about taking input, evaluating it by doing computation, and then generating output. Is there a fundamental theory? Another member of our team (Jonathan Gorard) has written two 60-page technical papers. But why should that be true? In other words, this is a rule that tries to sort a string into alphabetical order, two characters at a time. any event) in a causal graph. In other words, from the property of causal invariance, we’re able to derive relativity. The project was launched in April 2020[3][4][5] with the main contributors being Stephen Wolfram, Jonathan Gorard and Max Piskunov. 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. I’m looking forward to being deeply involved. And roughly the reason this works is that different foliations of rulial space correspond to different choices of sequences of rules in the rule-space multiway graph—which can in effect be set up to “compute” the output that would be obtained with any given description language. And that suggests the bizarre possibility that—just maybe—something like the angular structure of the cosmic microwave background or the very large-scale distribution of galaxies might reflect the discrete structure of the very early universe. One might imagine that—once we know the rule for some system—then with all our computers and brainpower we’d always be able to “jump ahead” and work out what the system would do. We found an outline derivation of my late friend and mentor Richard Feynman’s path integral. Needless to say, people have thought that space might ultimately be discrete ever since antiquity. And indeed the phenomenon of computational irreducibility implies that there is something definite and irreducible “achieved” by this process. Normally in physics one puts in relativity by the way one sets up the mathematical structure of spacetime. 1:12:01 – Wolfram Physics Project 1:29:53 – Emergence of time 1:34:11 – Causal invariance 1:53:03 – Deriving physics from simple rules on hypergraphs 2:07:24 – Einstein equations 2:13:04 – Simulating the physics of the universe 2:17:28 – Hardware specs of the simulation 2:24:37 – Quantum mechanics in Wolfram physics model Authors: Stephen Wolfram. Note: From 1987 to 2020, Stephen Wolfram’s intellectual efforts have not primarily been reported in academic articles. But to make everything work we’re going to have to build on a lot of what my physicist friends have been working so hard on for the past few decades. 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 in our models they’re not—even though, as we’ll see, relativity comes out just fine. But now we need to finish the job. The causal graph defines what event has to happen before what. We can identify two kinds of directions: spacelike and timelike. Underneath, it’s a bunch of discrete, abstract relations between abstract points. The successive pink lines effectively mark off what the observer is considering to be successive moments in time. But the important thing we see is that at the end all the paths merge, and we get a single final result: the sorted string AAABBB. © Stephen Wolfram, LLC He's only playing a game of applying rules to make structures, then attempting to find analogies between those structures and the actual physics … But in our models, the situation is quite different. We can ask about other strange phenomena from general relativity. Could it in fact be that underneath all of this richness and complexity we see in physics there are just simple rules? Instead of giving a flat estimate of dimension (here equal to 2), we have something that dips down, reflecting the positive (“sphere-like”) curvature of the surface: What is the significance of curvature? Of course, in some sense, it’s not “really” that surface: it’s just a hypergraph that represents a bunch of abstract relations—but somehow the pattern of those relations gives it a structure that’s a closer and closer approximation to the surface. We’re dividing the causal graph into leaves or slices. Stephen Wolfram recently announced his new Physics Project, an attempt to rethink how we do physics in terms of simple operations on abstract structures. And in direct analogy to what happens in special relativity, as you get closer to moving at the maximum speed you inevitably sample things more slowly in time—and so you get time dilation, which means that your “quantum evolution” slows down. So in the end we have two contributions to the “volumes” of our light cones: one from “pure curvature” and one from energy-momentum. What does it mean to make a model for the universe? Actually, it’s rather straightforward. For example, there are closed timelike curves, sometimes viewed as allowing time travel. Stephen Wolfram, a controversial physicist and computer scientist, has united relativity, quantum mechanics and computational complexity in a single theory of everything. And the exciting thing is that in our models, there’s an obvious resolution. Now we can go back and also talk about how curvature interacts with mass and energy in space. There are some other strange possibilities too. I’m exhilarated that I can understand any of it! Follow project development as it is livestreamed. But, OK, let’s say we find that our universe can be described by some particular rule. But for now let’s just recall that particles (like electrons) in our models basically correspond to locally stable structures in the hypergraph. The “core feature” of each particle will be some kind of locally stable structure in the hypergraph (a simple analogy might be that it’s a lump of nonplanarity in an otherwise planar graph). So where might oligons be now? We’re glossing over lots of details here. But the process of measuring dimension shows an example of how we can start making “physics-connectable” statements about the behavior of our rules. If you know about special relativity, you’ll recognize a lot of this. Then the obvious immediate question would be: why that rule, and not another? 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. But pretty soon I got swept up in building Wolfram|Alpha, and the Wolfram Language and everything around it. 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. But in all this complexity, there’s something wonderful that happens. The order in which we state the relations doesn’t matter (although the order within each relation does matter). Why is it called what it’s called? Which in a sense is another way of saying that there’s lots of nice mathematics to do in actually making the derivation rigorous, and understanding exactly when it’ll apply, and so on. And the surprise is that it seems a bunch of them do. To help see how this works here’s a very toy version of a multiway causal graph: Each point is an event that happens in some hypergraph on some branch of a multiway system. So what this all means is that if we look at the growth rates of spherical balls in our hypergraphs, we can expect two contributions: a leading one of order rd that corresponds to effective dimension, and a “correction” of order r2 that represents curvature. Here’s an example of a multiway causal graph for just a few steps of a very simple string substitution system—and it’s already pretty complicated: But in a sense the multiway causal graph is the most complete description of everything that can affect the experience of observers. In the previous section we said that we wanted to find a rule that we could in a sense connect with the description language that we use for the universe. But here what’s important about it is that it’s what’s going to make our universe, and everything in it. I’ve written a 448-page technical exposition (yes, I’ve been busy the past few months!). Mr Wolfralm has always stunned me with his interesting and novel new ways of looking at things and the results of these, i.e. So even though we may be dealing with hypergraphs, not strings, and we may have a rule that shows all kinds of complicated behavior, if it ultimately has causal invariance, then (with various technical caveats, mostly about possible wildness in the causal graph) it will exhibit relativistic invariance, and a physics based on it will follow special relativity. The Wolfram Physics Project is a project launched by computer scientist and physicist Stephen Wolfram to find the fundamental theory of physics. Causal invariance says that paths in the causal graph that diverge should always eventually merge. (The actual expression is roughly where the are timelike vectors, etc.). We started understanding how quantum mechanics works. In our models, closed timelike curves are inconsistent with causal invariance. And see if we can finally deliver the answer to how our universe fundamentally works. This would be an interesting resolution to the age-old debate about whether the universe is discrete or continuous. Of course, as with physical experiments, it matters how we define and think about our experiments, and in effect what description language we use. Thank you so much for making this discovery “accessible” to us all. 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. 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. Thanks for putting this together. Yes, it’s structurally discrete, but the scale of discreteness relative to our scale is always getting smaller and smaller. In designing a computational language what one is really trying to do is to create a bridge between two domains: the abstract world of what is possible to do computationally, and the “mental” world of what people understand and are interested in doing. But now we can do something directly analogous in the causal graph: start at some point, and follow possible sequences of t connections. Love from Germany. Then follow r hyperedges in all possible ways. Of course, there are lots of details about this—which no doubt depend on the particular underlying rule. Something could also be represented by multiple values. And a crucial idea in our model is in a sense just to do all of them. For example, we might wonder what the “zero of energy” is. “But how will you ever get quantum mechanics?”, physicists would always ask me when I would describe earlier versions of my models. They’d probably interact very very weakly with other things in the universe. For example, everything, nothing, and something. 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. And in that theory gravity is associated with curvature in space. But actually the multiway graph gives us that. Anyway, congratulations for discovering new ways to fascinate humans! What an incredible moment to witness! You could expand one of the powers first, then multiply things out. But there’s more to it. Here’s an example of a wonderful correspondence: curvature in physical space is like the uncertainty principle of quantum mechanics. And in the context of our models they’re just different facets of the same idea. I’d just thought of it as an attribute that things (atoms, photons, whatever) can have. Start at some point in the hypergraph. It’s a phenomenon that’s implied by the add-ons to the standard formalism of quantum mechanics that describe measurement. But if the rule we find to describe our universe is simple, wouldn’t that simplicity be a sign of “specialness”? But when we talk about making a model, what we really mean is that we want to have a representation of the universe that somehow connects it to what we humans can understand. I’ll be happy to learn about the outcome as I believe I am unfortunately not in a position to effectively put a worthwhile contribution to this. Adding numbers with parenthesis in any order yields the same result. I have no doubt that with time you will discover the centre of whats fundamental. Fabienne Lang, Interesting Engineering. Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist who is the founder and CEO of Wolfram Research, a company behind 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. OK, so given all this, what’s it going to take to find the fundamental theory of physics? And that’s what’s happening in our little sorting algorithm above. The rule just says to find two adjacent connections, and if there are several possible choices, it says nothing about which one. What we’re seeing here are the results of applying rules a few thousand times; in our actual universe they may have been applied 10500 times so far, or even more. And it’s the same story: the geodesic is the shortest path between two points in the graph (or hypergraph). And how that works is bound up with the question of what the zero of energy is, which in our model relates to what features of the evolving hypergraph just have to do with the “maintenance of space”, and what have to do with “things in space” (like matter). There are a variety of consequences. But in the third example, space is in a sense very connected. And that’s something that’s burnt into the mathematical structure of the theory. But this isn’t just a project for me or our small team. In many ways it’s the ultimate question in natural science: How does our universe work? If there’s a match, then replace these two relations with the four relations on the right. In our models, we can explicitly see that happen in the causal graph. He is the brains behind Wolfram Alpha, a website that tries to answer questions by using algorithms to sift through a massive database of information.He is also responsible for Mathematica, a computer system used by scientists the world over.. Last week, Wolfram launched a new venture: the Wolfram Physics … The traditional approach in natural science (at least over the past few centuries) has tended to be: start from what you know about whatever system you’re studying, then try to “reverse engineer” what its rules are. One always has to keep doing experiments, though. The reference frames of special relativity are now our quantum observation frames. 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. But it’s just conceivable that something like a breaking of symmetry associated with the first few hypergraphs might somehow survive. After all, we already have two extraordinarily successful physical theories. But then there are both spacelike and branchlike relationships, where the event affects elements that are either “spatially” separated in the hypergraph, or “branchially” separated in the multiway system. (And, for example, this irreducibility is what I believe is responsible for the “encrypting” of initial conditions that is associated with the law of entropy increase, and the thermodynamic arrow of time.) like 2r). In our earlier discussion, we talked about constructing spherical balls by starting at some point in the hypergraph, and then following all possible sequences of r connections. 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. [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. And now we’re saying that the flux of causal edges specifically in the timelike direction corresponds to rest mass. We started off with a simple rule that just tells us how to transform collections of relations. As everything can be defined with a few simple rules, would It mean that all Knowledge, Past AND Future can be defined, for instance teleportation? And I’ve never seen anything that comes close. There’s a way of talking about it in the standard language of quantum mechanics: as we move in branchial space, we’re effectively getting “entangled” with more and more quantum states. (The constancy of ρ is in effect a reflection of the Principle of Computational Equivalence.). Thank you, Stephen Wolfram and the team! But what kinds of reference frames might observers set up in rulial space? So in other words, even though we in a sense had two paths of history that diverged in the multiway system, it took only one step for them to converge again. The universe in a sense had input at the very beginning, but now it’s just running an evaluation—and with all our different ideas of foliations and so on, we are sampling certain aspects of that ongoing evaluation. 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). If it is correct however, what has been learned or hypothesized about the underlying medium/structure for execution of these rules (OS? Stephen Wolfram Invites You to Solve Physics. Calculus has been built to work in ordinary continuous spaces (manifolds that locally approximate Euclidean space). Normally the area of a circle is πr2. The presence of energy effectively causes curvature in branchial space which causes the paths of geodesics through branchial space to turn. And every so often I’d wonder if they might be relevant for physics. Is it trivalent graphs? But actually what amounts to causal invariance has been seen before in various different guises in mathematics, mathematical logic and computer science. We can represent the rule as a transformation of graphs: The {2,3} and {2,4} relations get matched, and the rule replaces them with four new relations, so the result is: {{1, 2}, {3, 4}, {2, 4}, {2, 5}, {3, 5}, {4, 5}}. But in our models there’s in a sense nothing but space—and in a sense everything in the universe must be “made of space”. spacelike) to “vertical” (i.e timelike) distances on the causal graph. Or, put another way, just how simple is the rule for our universe going to end up being? What properties would these oligons have? 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. We don’t know if the precise details of how our rules are set up are correct, or how simple or not the final rules may be. Entrepreneur Stephen Wolfram is a unique egg. OK, so how does this work? It didn’t help that there was something that bothered me about my ideas. Or we can think of it as a hypergraph—or, in simple cases, a graph. I’ve often thought about writing a program which takes a simple set of rules and replicated them over and over. But now think about what happens when you try to make a rectangle in physical space by going in direction x first, then y, and then you do these in the opposite order. Not quite. And we can think of them as representing the correlation—or entanglement—of quantum states. 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… 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. But imagine making a multiway graph of absolutely everything that can happen—including all events for all possible rules. At the beginning of this piece, I talked about the rule, and showed the “first few steps” in applying it. Yes, the underlying structure of our models is different. Most likely lots of oligons would have been produced in the very early universe, but with their very weak interactions, they’d soon “drop out of thermal equilibrium”, and be left in large numbers as relics—with energies that become progressively lower as the universe expands around them. It’s an amazing unification that I have to say I didn’t see coming; it’s something that just emerged as an inevitable consequence of our simple models of applying rules to collections of relations, or hypergraphs. At least relative to the particles we currently know, such particles would have few hypergraph elements in them—so I’m referring to them as “oligons” (after the Greek word ὀλιγος for “few”). How does our universe work? And we also have a crucial piece of methodology that helps us: our ability to do explorations through computer experiments. It looks it’s “trying to make” something 3D. (Which is, by the way, presumably why we are fundamentally able to form a coherent view of physical reality at all.). Many pieces fit so elegant to let this work forgotten. But what then is time? But, OK, so what rules should we consider? Everything could be represented as 1 or infinity nothing could be represented by 0 or 1 because it is something or infinity. We’ve had mathematical idealizations and abstractions of it for two thousand years. Underneath, an observer is getting updated by some sequence of updating events. … In fact, even though the rule itself is completely deterministic, the structure it makes looks quite random. It’s just that—with some particular mode of description that we choose to use—there will be some definite rule that describes our universe. The project builds on Wolfram's previous research into computational systems, as explored in his book, A New Kind of Science. This is a big, complicated object. It’s always had a certain “you-are-not-expected-to-understand-this” air, though, coupled with “just-trust-the-mathematical-formalism”. You have achieved so much already. In the end our goal must be to build a bridge that connects our models to existing knowledge about physics. Back in my university PhD days, I discovered Mathematica and found a way to convince my university to purchase serial number 60 of it. ... How We Got Here: The Backstory of the Wolfram Physics Project April 14, 2020. Here I’ve used numbers, but all that matters is that the elements are distinct. Categories of articles by Stephen Wolfram. 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 even though that’s “really what’s going on”, to make sense of it, we can imagine our observers setting up internal “mental” models for what they see. So each “step” that we showed before actually consists of several individual “updating events” (where here newly added connections are highlighted, and ones that are about to be removed are dashed): But now, here is the crucial point: this is not the only sequence of updating events consistent with the rule. OK, so what about branchial space? Here are some of the things they do: Somehow this looks very zoological (and, yes, these models are definitely relevant for things other than fundamental physics—though probably particularly molecular-scale construction). We don’t (yet) know an actual rule that represents our universe—and it’s almost certainly not the one we just talked about. And maybe the limit from which it appears is not a clearly defined one …. So to really talk about it well, we have to invent something that’s kind of a generalization of calculus, that’s for example capable of dealing with curvature in fractional-dimensional space. But I want to expose everything as broadly as possible, so everyone can be involved in—and I hope inspired by—what I think is going to be a great and historic intellectual adventure. For new academic publications, see the Wolfram Physics Project.. 1975 But how exactly did the rule get applied? 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. Instead, even if you know the exact rule that a system follows, you may still not be able to work out what the system will do except by essentially just tracing every step it takes. And it turns out that we can think of them as being laid out in an abstract kind of space that we’re calling “branchial space”. [6] A book, A Project to Find the Fundamental Theory of Physics, was published about the project in June 2020. I call this maximum entanglement speed ζ (zeta) (ζ looks a bit like a “tangled c”). And before quantum mechanics, classical physics typically captured this in laws—usually equations—that would tell one what specifically a system would do. 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