And for 50 years people have almost universally assumed that there’s a crippling problem with models like that. It’s typically from physicist friends, and typically it’s some combination of, “Don’t waste your time working on that!” and, “Please don’t work on that.”. Of course you do. When it comes to deriving the Einstein Equations, one creates Ricci tensors by looking at geodesics in the network, and looking at the growth rates of balls that start from each point on the geodesic. On the contrary, such explanations are off-topic, as you should know by now. Sunny Singh: I’m not a star son, so I don’t understand that space well bollywood Updated: Oct 05, 2020, 16:59 IST They discuss what physics looks like from other people’s perspectives and why things sometimes behave differently. So then the question arises: could one of these simple programs in the computational universe actually be the program for our physical universe? Albert Gartinger 19:27, 4 October 2018 (UTC) Your interlocutor is under no obligation to explain anything here. So far all our discussions in special relativity have involvedthe motion of bodies in space over time. It makes a lot of sense in the formalism of Special Relativity, in which, for example, traveling at a different velocity is like rotating in 4-dimensional spacetime. Because if there’s a discrete network “underneath” space, then Euclid’s assumptions about points and lines that can exist anywhere in space simply aren’t correct. Nice article. Time is not governed by space nor is it dependent upon space. When Spacetime is twisted up into a knot, it stretches the surrounding material, as it is pulled into the knot. And to understand this, we have to do something a bit similar to what Einstein did in formulating Special Relativity: we have to make a more realistic model of what an “observer” can be. Absolutely not. And though it was described in simple language rather than physics-speak, I managed to cover the highlights of it in Chapter 9 of the book—giving some of the technical details in the notes at the back. To describe what happens, physicists need to go beyond space and time. And neither can Stephen Hawking. And quite likely such an investigation will have interesting spinoffs. Telling if they actually are our universe is a difficult matter. But what about in a network? It’ll need serious, sophisticated physics—with understanding of the upper reaches of quantum field theory and perhaps string theory and things like spin networks. But now things get a bit complicated. So what’s the alternative? So what about spacetime and Special Relativity? As I write this, I realize how easily I still fall into technical “physics speak”. In other words, even though at the lowest level space and time are completely different kinds of things, on a larger scale they get mixed together in exactly the way prescribed by Special Relativity. All these things have to emerge. Neither can I, even though it’s reality. And who knows: maybe it will be easier than we think, and we’ll look back and wonder why it wasn’t tried long ago. Here, as I figured out in the mid-1990s, something exciting happens: as soon as there’s causal invariance, it basically follows that there’ll be Special Relativity on a large scale. The whole story is somewhat complicated. Because of the phenomenon I call “computational irreducibility”—which implies that even though one may know the rule and initial condition for a system, it can still require an irreducible amount of computational work to trace through every step in the behavior of the system to find out what it does. I thought about this for years, and looked at all sorts of computational and mathematical formalisms. In a sense, though, this was always just a hobby, done alongside my “day job” of leading our company and its technology development. If the network is behaving like it’s d-dimensional, then the number of nodes in that “ball” will be about rd. But the good news is that an incredible range of systems, even with extremely simple rules, work a bit like the digits of pi, and generate what seems for all practical purposes random. Now, do you want to see these two concepts, and the connections between space and time (spacetime), explained by two adorably dorky scientists? When our emotions are high, we revert back to our own language. Nature does seem to be telling us, as Stephen says over and over, that complicated structures arise from simple rules, but there’s no reason why that might not be multiple, nested algorithms or networks, each begetting something richer and stranger than the components of the network itself. A simple hypothesis is to assume that there’s some kind of local rule, which says, in effect that if you see a piece of network that looks like this, replace it with one that looks like that. But that gets pretty complicated. Ultimately, the ball would follow a so-called parabola, as though it had been thrown along at the same speed as the train. From almost nothing, it’s possible to derive Einstein’s Equations. It’s easy to see similar things in cellular automata on a lattice. Yes, one can find rules that give behavior which on a large scale doesn’t show obvious signs of the lattice. But that’s a risk you take when you do a project where in effect nature decides what’s right. And as a result of my work on A New Kind of Science, I became convinced that this might be actually be possible—and that this might be the right decade to do it. Or certain areas of mathematics have advanced further. I think this is pretty exciting. Because there’s a theorem (Bell’s Theorem) that says that unless there’s instantaneous non-local propagation of information, no such “hidden variables” model can reproduce the quantum mechanical results that are observed experimentally. I don't understand by popnauts: Listen to songs by popnauts on Myspace, a place where people come to connect, discover, and share. Time was thought to pass at the same rate for all observers, regardless of where they were or how fast they were moving. Of course this would be an exciting day for science. It’s pretty clear what “non-locality” means in ordinary space with a definite dimension. Roughly what happens is that different “reference frames” in Special Relativity—corresponding, for example, to traveling at different velocities—correspond to different detailed sequencings of the low-level updates in the network. But it would raise plenty of other questions. One has to look at shortest paths—or geodesics—in the network. We have observed that Space-time stretched, compressed, and just wiggles. Both were described by coordinates, and in some mathematical formalisms, both appeared in related ways. Dr. Mark’s big pitch is that diversity demands attention, especially in situations like a long space flight during which people have to understand their differences and get along. Posted in: Historical Perspectives, Physics. But the exciting thing is that remarkably quickly one finds rules that aren’t obviously not our universe. OK, so let’s say that underneath space there’s a network. Or some more issues in physics have been clarified. (I think it must be that I learned physics when I was so young…) But suffice it to say that at a high level the exciting thing is that from the simple idea of networks and causal invariant replacement rules, it’s possible to derive the Equations of General Relativity. We don’t understand things all the time because ‘people’ isn’t our first language. Or would it be much, much smaller? You just watched 2001: A Space Odyssey… but you don’t really know what just happened.. Last week, for the 3rd time, I saw 2001 (but this time … How does this network evolve? But unlike building a piece of technology, or exploring an area of science, the definition of the project isn’t under one’s control. But after seeing what’s out there in the computational universe—and seeing some other examples where amazing things were found just by a search—I’ve changed my mind. I’m actually not too worried about this. on that basis. Time always passed at the same rate, and was absolute as well. And there’s a simpler possibility: maybe in some sense everything in the universe is just “made of space”. And I’m hoping that before too many more anniversaries of General Relativity have gone by we’ll finally know what spacetime really is. There’ll be useful support from existing fields. But sometime in 1988—around the time the first version of Mathematica was released—I began to realize that if I changed my basic way of thinking about space and time then I might actually be able to get somewhere. I just don't understand the purpose of the bottom number in the time signature if, for example 4/4 is telling me the crotchet is the kind of beat, and yet crotchets don't need to be used. First, it’s worth noting that my underlying networks not only have no embedding in ordinary space intrinsically defined, but also don’t intrinsically define topological notions like inside and outside. General Relativity is a great theory—but we already know that it cannot be the final theory. ... put them in the dishwasher, and marinate in them. And one could imagine a theory in which all threads are followed—and the universe in effect has many histories. Suggest trying out your network theory using a point of this character. First of all, how could the apparent continuity of space on larger scales emerge? One of the key realizations that led to General Relativity 100 years ago was that Euclid’s fifth postulate (“parallel lines never cross”) might not be true in our actual universe, so that curved space is possible. Indeed, the history of physics so far might make us doubtful—because it seems as if whenever we learn more, things just get more complicated, at least in terms of the mathematical structures they involve. One has to see how to do everything not just in space, but in networks evolving in time. He thought that perhaps particles, like electrons, could be associated with something like black holes that contain nothing but space. Consciousness emerges from a neural network but cannot be adequately described by explaining or inspecting the network. If the network behaves like flat d-dimensional space, then the number of nodes will always be close to rd. And it could be that I’m simply wrong about how our universe works. So here’s the final result. In qualitative terms, they might not be that different from Kelvin’s “knots in the ether”. The formula is that M(matter)= Spacetime•C(squared). For Another Eden: The Cat Beyond Time and Space on the Android, a GameFAQs message board topic titled "I don't understand how HP-MP badge works". Is time treated as a constant so time is the same? Space itself was a fixed entity, sort of like a Cartesian grid: a 3D structure with an x, y and z axis. There’s going to be lots of algorithm development for things like network evolution, and for analysis. And actually, there’s a simple test for the effective dimension of a network. Physics at the end of the nineteenth century found itself in crisis:there were perfectly good theories of mechanics (Newton) and electromagnetism(Maxwell), but they did not seem to agree. Now remember, the network is just a collection of nodes and connections. Though there are also other things I want to do. But here’s the thing: just because the underlying rules treat space and time very differently, it doesn’t mean that on a large scale they can’t effectively behave similarly, just like in current physics. The ideas in this post have been developed much further in the Wolfram Physics Project, which you can read more about in the project announcement. Preface. Here the news is very good too: subject to various assumptions, I managed in the late 1990s to derive Einstein’s Equations from the dynamics of networks. Scientists propose that clocks measure the numerical order of material change in space, where space is a fundamental entity; time itself is not a fundamental physical entity. And until we actually find a serious candidate rule for our universe, it’s probably not worth discussing these things much. Are we afraid of infinitesimal continuity as it points to infinity “within”? I’m sure it’ll need abstract graph theory, modern geometry and probably group theory and other kinds of abstract algebra too. So what happens if one actually starts doing such a search? I definitely want to. One just thinks of space as a mathematical construct that serves as a kind of backdrop, in which there’s a continuous range of possible positions at which things can be placed. Even more confusing, we sometimes choose to be away from people we really like. Historically, space and time were thought of as separate entities. It’s been interesting over the years to ask my friends whether I should work on fundamental physics. Which network it is must be determined by some kind of constraint: our universe is the one which has such-and-such a property, or in effect satisfies such-and-such an equation. Read “The Binary Universe” – A Theory of Time, https://uppbooks.com/shop/product/the-binary-universe-a-theory-of-time/. Time is the fundamental here and space, the emergent. Simple as the experiment may sound, it set off a debate about the nature of space, time, motion, acceleration, and force that continues to this day. Still, the possibility exists that one could just find a simple rule—and initial condition—that one could hold up and say, “This is our universe!” We’d have found our universe in the computational universe of all possible universes. But then along came Einstein’s Special Theory of Relativity—and people started talking about “spacetime”, in which space and time are somehow facets of the same thing. To me, modern theories of everything give up before they begin by plugging in quantum mechanics at the bottom level. And Sir Isaac had just the experiment to prove it: a spinning bucket of water. But what I discovered is that in the computational universe even extremely simple programs can actually show behavior as complex as anything (a fact embodied in my general Principle of Computational Equivalence). Thanks for your comment, Ken! I was pretty organized in what I did, getting intuition from simplified cases, then systematically going through more realistic cases. It’s defined by our universe. From their perspective (the perspective of the person on the boat, the ball just falls straight down. At the beginning it might have looked hopeless: how could a network that treats space and time differently end up with Special Relativity? And one needs an underlying data structure that’s as flexible as possible. See also the Wolfram Physics Project Bulletins for informal updates and commentary on the project’s progress. For example, these universes can start from effectively infinite numbers of dimensions, then gradually settle to a finite number of dimensions—potentially removing the need for explicit inflation in the early universe. Finding the fundamental theory of physics, though, is a project of a rather different character than I’ve done before. Ultimately, the perspective of the original, stationary camera (which will witness a plethora of things coming and going and moving about) can also be analyzed from the perspective of someone moving along at a steady rate. But nothing I have seen suggests that there are any immediate roadblocks—other than putting the effort and resources into trying to do it. Now think about all those little network updatings that are happening. I’ve been thinking about the physics of space and time for a little more than 40 years now. It was an interesting idea. And—if things go well—it’ll need an understanding of a diverse range of physics experiments. But I suspect the biggest challenges will be in building the tower of new theory and understanding that’s needed to study the kinds of network systems I want to investigate. But after the book was finished in 2002, I started working on the problem of physics again. And actually, I don’t know of any other model in which one can successfully derive Special Relativity from something lower level; in modern physics it’s always just inserted as a given. Before studying the computational universe of simple programs I would have assumed that this would be crazy: that there’s no way the rules for our universe could be simple enough to find by this kind of enumeration. I suggest the the single bit of matter is created in this manner. It’s wonderful to be able to derive General Relativity. And that’s interesting, because the Ricci scalar is precisely something that occurs in Einstein’s Equations. A network—or graph—just consists of a bunch of nodes, joined by connections. There are plenty of encouraging features, though. The particles in the universe don’t just all do their own thing; they follow a definite set of common laws. But how could this be what space is made of? But that really was what it was doing: enumerating possible rules of certain types, and trying to see if their behavior satisfied certain criteria that could make them plausible as models of physics. Time was the same everywhere. Basically, I just don't understand how time works with space as a fourth dimension. Because there might be lots of places in the network where the rule could apply. I think there are enough clues from existing physics—as well as from anomalies attributed to things like dark matter—that one will be able to tell quite definitively if one has found the correct theory. OK, so it’s conceivable that some network-based model might be able to reproduce things from current physics. I’ve been fascinated by this research program ever since reading NKS. Are they fundamental particles? Meanwhile, it had been understood that there were different types of discrete atoms, corresponding to the different chemical elements. Except for one theory, Binary Universe Theory, or “B.U.T.” Here, time emerges from the fundamental energy field, a double wave of energy made up us Plank times, which themselves are made up of oscillating energy quanta. When he told me he need space because I don't understand what space is, I thought he wanted to break up with me, so, I challenge him alot and I make some statement I was not suppose to use on him. Most of what I’ve said here I had actually figured out by around 1999—several years before I finished A New Kind of Science. Maybe all that has to exist in the universe is the network, and then the matter in the universe just corresponds to particular features of this network. But just how simple might the ultimate theory for the universe be? Have you made more progress since writing this post? I found it a bit amusing to say I had a computer in my basement that was searching for the fundamental theory of physics. I write about a … And in fact, much as I like General Relativity as an abstract theory, I’ve come to suspect it may actually have led us on a century-long detour in understanding the true nature of space and time. They don’t understand how we could enjoy being alone, period. It’s a bit like what happens in a fluid, like water. In physics, spacetime is any mathematical model that combines space and time into a single continuum. But—as noted, for example, by early theologians—one very obvious feature of our universe is that there is order in it. Light was known to be anelectromagnetic phenomenon, but it did not obey the same lawsof mechanics as matter. As we all know, Space is where things happen. Or other pathologies. Are you familiar with causal dynamic triangulation? In deriving mathematical results, it’s important to be able to take certain kinds of averages. Forty years—and several tens of billions of dollars’ worth of particle accelerators—later there’s still no discreteness in space that’s been seen, and the limit is about 10-22 meters (or 100 yoctometers). In a sense its definition of success is much harsher: one either solves the problem and finds the theory, or one doesn’t. For many years I had been interested in the problem of computational knowledge, and in building an engine that could comprehensively embody it. Encouraged by this success, I then began to wonder if perhaps the things I’d found might be relevant to that ultimate of scientific questions: the fundamental theory of physics. But my current guess is that it’d be something much more bizarre, such as that with respect to observers in a universe, all of a large class of nontrivial possible universe rules are actually equivalent, so one could pick any of them and get the exact same results, just in a different way. The effects of absolute space are quite observable. But if it behaves like curved space, as in General Relativity, then there’s a correction term, that’s proportional to a mathematical object called the Ricci scalar. But there’s an important footnote. The oscillations are what produces the wave. And there was another “distraction”. So if the behavior of the universe is determined by a simple program, what’s the basic “data structure” on which this program operates? How might we set about finding such a model that actually reproduces our exact universe? I used to be a space scientist, and now I'm a writer, although for a time the two careers ran in parallel. Where Did Combinators Come From? This conceptual circularity creates weird mathematical difficulties. Let’s say we could represent it as a program, say in the Wolfram Language. In the abstract it’s far from obvious that there should be a simple, ultimate theory of our universe. Try as they might, they run into nothingness when they try to peer deeply into their reality. I don’t feel any force, even as I accelerate toward the ground! Time, on the other hand, is when things happen. They drop a ball on the deck of the boat. But, OK, if space is a network, what about all the stuff that’s in space? But in thinking about space as a network, there’s a related idea: maybe particles just correspond to particular structures in the network. Of course I don’t know how difficult the project is, or whether it will even work at all. The traditional instinct would be to start from existing physics, and try to reverse engineer rules that could reproduce it. Time/Space … Is it the right time to actually try doing this project? But there was no notion that space and time were in any sense “the same thing”. At the beginning, as a young theoretical physicist, I mostly just assumed Einstein’s whole mathematical setup of Special and General Relativity—and got on with my work in quantum field theory, cosmology, etc. In essence, one way of thinking about physics is imagining a stationary camera. One thing is clear: if the program is really going to be extremely simple, it’ll be too small to explicitly encode obvious features of our actual universe, like particle masses, or gauge symmetries, or even the number of dimensions of space. Because space consists of 3 dimensions, and time is 1-dimensional, space-time must, therefore, be a 4-dimensional object. I’m not sure. One puts remarkably little in, yet one gets out that remarkable beacon of 20th-century physics: General Relativity. I accumulated the equivalent of thousands of pages of results, and was gradually beginning to get an understanding of the basic science of what systems based on networks can do. Why do something abstract and theoretical when you can do something practical to change the world?”, There’s also a third class of responses, which I suppose my knowledge of the history of science should make me expect. Just start from a node, then look at all nodes that are up to r connections away. But—as noted, for example, by early theologians—one very obvious feature of our universe is that there is order in it. In the early days of quantum mechanics, it was actually assumed that space would be quantized like everything else. It’s also likely to need methods that come from statistical physics and the modern theoretical frameworks around it. Now, at 2:47 AM 9/17/2016, Alaskan standard was the same here as at Mars, and Betelgeuse, and Orion, etc. As it happens, nearly 100 years earlier there’d been somewhat similar ideas. For instance, the little 't' that physicists use to denote time drops out of their equations, leaving them at a loss to explain change in the world. But even though such a structure works well for models of many things, it seems at best incredibly implausible as a fundamental model of physics. But once I embark on a project, I commit myself to finding a way make it succeed, even if it takes many years of hard work to do so. Experiments by Albert A. Michelson (1852-1931) andothers in the 1880s showed that it always traveled with the same velocity,regardless of the speed of its source. But by the time one’s reproducing all the seemingly arbitrary masses of particles, and other known features of physics, one will be pretty sure one has the correct theory. In the usual formulation of physics, space is a backdrop, on top of which all the particles, or strings, or whatever, exist. As we all know, Space is where things happen. But within the formalism of General Relativity, Einstein could never get this to work, and the idea was largely dropped. It’ll need an understanding of General Relativity and cosmology. Theories of everything give up before they begin by plugging in quantum at. Us understand the universe as a whole discussion to be able to quickly recognize subtle that. Said Berman discuss the Law of one principles he thought that perhaps particles, like water ever since reading.. 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