The Wolfram Physics Project Q&A : (3) Relations to Other Approaches

<!doctype html> <html lang="en"> <head>  <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <title>The Wolfram Physics Project Q&A : (3) Relations to Other Approaches</title> <meta name="description" content="Answers to questions about relations to other approaches related to Stephen Wolfram’s project and new approach to find the fundamental theory of physics."> <meta property="og:title" content="The Wolfram Physics Project Q&A : (3) Relations to Other Approaches"> <meta property="og:description" content="Answers to questions about relations to other approaches related to Stephen Wolfram’s project and new approach to find the fundamental theory of physics."> <meta name="twitter:title" content="The Wolfram Physics Project Q&A : (3) Relations to Other Approaches"> <meta name="twitter:description" content="Answers to questions about relations to other approaches related to Stephen Wolfram’s 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C3.21078644,16.3321068 3.58578644,16.5 4,16.5 L6.5,16.5 L7.35355339,20.9393398 L11.7918591,16.5 L20,16.5 C20.4142136,16.5 20.7892136,16.3321068 21.0606602,16.0606602 C21.3321068,15.7892136 21.5,15.4142136 21.5,15 L21.5,5 C21.5,4.58578644 21.3321068,4.21078644 21.0606602,3.93933983 C20.7892136,3.66789322 20.4142136,3.5 20,3.5 Z" id="Combined-Shape-Copy" stroke="#fff"></path> <polygon id="Line" fill="#fff" fill-rule="nonzero" points="17 9 17 10 5 10 5 9"></polygon> <polygon id="Line" fill="#fff" fill-rule="nonzero" points="15 11 15 12 5 12 5 11"></polygon> <polygon id="Line" fill="#fff" fill-rule="nonzero" points="11 13 11 14 5 14 5 13"></polygon> <polygon id="Line" fill="#fff" fill-rule="nonzero" points="19 7 19 8 5 8 5 7"></polygon> </g> </svg> Ask a question </a> </div> <div class='tagbuttons'> <a class="tag" data-tag="all" href="/questions/main/">All</a> <a class="tag" data-tag="general" href="/questions/general">(1) General</a> <a class="tag" data-tag="scientific-general-interest" href="/questions/scientific-general-interest">(2) Scientific General Interest</a> <a class="tag on" data-tag="relations-to-other-approaches" href="/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> <a class="tag" data-tag="spacetime-relativity" href="/questions/spacetime-relativity">(4) Spacetime / Relativity</a> <a class="tag" data-tag="quantum-mechanics" href="/questions/quantum-mechanics">(5) Quantum Mechanics</a> <a class="tag" data-tag="computation-theory" href="/questions/computation-theory">(6) Computation Theory</a> </div> </div> </div> </header> <section class="section"> <div class="inner"> <div><h1 id="category">(3) Relations to Other Approaches</h1><span id="count">(10)</span></div> <div id="posts" class="grid heirs-width-1-2 heirs-width-full__600"> <div class="project relations-to-other-approaches" data-position="normal" data-date="2019-05-02 17:34:57"> <p class="date">May 2, 2019</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/is-the-project-related-to-sacred-geometry/">Is the project related to sacred geometry?</a></h2> <div class="introtext" data-text="<p>Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. <a href="#more" class="more chevron-after">Read more</a>"> Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches spacetime-relativity quantum-mechanics computation-theory" data-position="normal" data-date="2020-03-11 18:39:19"> <p class="date">March 11, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/are-your-models-consistent-with-the-erepr-conjecture/">Are your models consistent with the ER=EPR conjecture?</a></h2> <div class="introtext" data-text="<p>Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. In other words, there exists a natural duality between spacetime and branchtime, with connections between distinct points in the spacetime causal graph (which correspond to Einstein&ndash;Rosen bridges) behaving in a fundamentally similar way to connections between distinct points in the multiway evolution graph (which correspond to quantum entanglements).</p> <p>More precisely, a formal statement of the ER=EPR conjecture is that the Bekenstein&ndash;Hawking entropy of a pair of entangled black holes is equivalent to their entanglement entropy. If Hawking radiation effects occur as a result of branch pairs that fail to reconverge as a consequence of disconnections in the multiway causal graph, the ER=EPR conjecture is really just a rather elementary statement about the geometry of branchtime (in other words, it states that the natural distance metric in branchtime is the entanglement entropy of pairs of microstates, which one can prove directly from the properties of the Fubini&ndash;Study metric tensor).</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. <a href="#more" class="more chevron-after">Read more</a>"> Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> <a class="tag" data-tag="computation-theory" href="https://www.wolframphysics.org/questions/computation-theory">(6) Computation Theory</a> </div> </div> <div class="project relations-to-other-approaches spacetime-relativity quantum-mechanics" data-position="normal" data-date="2020-03-13 00:00:00"> <p class="date">March 13, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/what-do-your-models-imply-regarding-the-black-hole-information-paradox/">What do your models imply regarding the black hole information paradox?</a></h2> <div class="introtext" data-text="<p>The maximum rate of quantum entanglement (i.e. the natural propagation velocity of geodesics in the multiway evolution graph) is, in general, much higher than the speed of light (i.e. the natural propagation velocity of geodesics in the purely relativistic causal graph); however this ceases to be the case in the presence of a sufficiently high mass density in spacetime (i.e. in the presence of a sufficiently high density of causal edges in the multiway causal graph), such as near a black hole.</p> <p>Therefore, a black hole in the multiway causal graph may be characterized by the presence of two distinct horizons: a standard event horizon corresponding to regular causal disconnection, and an entanglement event horizon corresponding to multiway disconnection, which always lies strictly on the exterior of the causal event horizon. As such, from the point of view of an external observer in the multiway causal graph watching an infalling object to a black hole, the object will appear to &#8220;freeze&#8221; (due to quantum Zeno effects that are the multiway analog of time dilation) at the entanglement horizon, and will never get close to the true causal event horizon. Since Hawking radiation (which occurs as a consequence of non-convergent branch pairs in the multiway evolution graph) is emitted from the entanglement horizon and not the causal event horizon, the particles that get radiated from the black hole may be perfectly correlated with the information contained within the infalling object, without any apparent or actual violation of special relativity (since no information ever crossed a spacetime event horizon), thus resolving the black hole information paradox.<br /> This resolution is formally quite similar to the standard resolution to the black hole information paradox implied by the holographic principle and the AdS/CFT duality.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The maximum rate of quantum entanglement (i.e. the natural propagation velocity of geodesics in the multiway evolution graph) is, in general, much higher than the speed of light (i.e. the natural propagation velocity of geodesics in the purely relativistic causal graph); however this ceases to be the case in the presence of a sufficiently high mass density in spacetime (i.e. <a href="#more" class="more chevron-after">Read more</a>"> The maximum rate of quantum entanglement (i.e. the natural propagation velocity of geodesics in the multiway evolution graph) is, in general, much higher than the speed of light (i.e. the natural propagation velocity of geodesics in the purely relativistic causal graph); however this ceases to be the case in the presence of a sufficiently high mass density in spacetime (i.e. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project relations-to-other-approaches spacetime-relativity quantum-mechanics" data-position="normal" data-date="2020-03-13 00:00:00"> <p class="date">March 13, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/are-your-models-consistent-with-the-holographic-principleads-cft-correspondence/">Are your models consistent with the holographic principle/AdS-CFT correspondence?</a></h2> <div class="introtext" data-text="<p>They certainly seem to be! Indeed, as discussed in the answer about implication for the black hole information paradox, the structure of the multiway causal graph seems to imply a form of the holographic principle in a very natural way.<br /> Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, as well as the structures of the (purely relativistic) causal graphs corresponding to each branch of multiway evolution. Therefore, one can imagine &#8220;walling off&#8221; a certain bundle of causal edges in the multiway causal graph corresponding to some particular branch of multiway evolution, such that all of the causal edges inside the boundary of the wall correspond to edges in a purely relativistic causal graph (i.e. they designate causal relations between events in spacetime), whilst all of the causal edges intersecting the boundary of the wall correspond to edges in a purely quantum mechanical multiway graph (i.e. they designate causal relations between events in branchtime). As such, one immediately obtains a duality between the bulk gravitational theory on the interior of the wall, and the boundary quantum mechanical theory on the surface of the wall, just as in AdS/CFT.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="They certainly seem to be! Indeed, as discussed in the answer about implication for the black hole information paradox, the structure of the multiway causal graph seems to imply a form of the holographic principle in a very natural way.<br /> Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, <a href="#more" class="more chevron-after">Read more</a>"> They certainly seem to be! Indeed, as discussed in the answer about implication for the black hole information paradox, the structure of the multiway causal graph seems to imply a form of the holographic principle in a very natural way.<br /> Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-14 00:00:00"> <p class="date">March 14, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-homotopy-theory-derived-geometry-and-higher-category-theory/">How do your models relate to homotopy theory, derived geometry and higher category theory?</a></h2> <div class="introtext" data-text="<p>The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. As such, a Wolfram model system is really just an F-coalgebra of the power set functor.<br /> The relationship to higher-order mathematics, specifically homotopy theory and higher category theory, and their geometrical incarnation in the form of derived geometry, is somewhat more speculative. A possible connection exists via the &#8220;snake states&#8221; of multiway evolution, as described in our answer to the question about string theory above. The essential idea here would be to use the so-called &#8220;cobordism hypothesis&#8221;—a theorem which implies that functors on monoidal (<span class="special-character Infinity">&#8734;</span>, <em>n</em>)-categories are entirely determined by their values on a single point, corresponding to an <em>n</em>-vector space of states—to deduce, for instance, that whilst the evolution of a single eigenstate through the multiway evolution graph may be described by a 1-category of spaces of states, the evolution of a maximally-consistent snake state may be described by a higher-order <em>n</em>-category of <em>n</em>-modules.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. <a href="#more" class="more chevron-after">Read more</a>"> The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-15 00:00:00"> <p class="date">March 15, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-twistor-theory/">How do your models relate to twistor theory?</a></h2> <div class="introtext" data-text="<p>Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory.</p> <p>The twistor correspondence, at least in Penrose&#8217;s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. twistor space) and massless Yang–Mills fields on Minkowski space. Mathematically speaking, the twistor space is the Grassmannian of lines in complexified Minkowski space, and the massless Yang–Mills fields correspond to the Grassmannian of planes in the same space. The correspondence space is therefore the Grassmannian of lines in planes in complexified Minkowski space, and it somehow encodes both the quantum mechanical structure of the Yang–Mills fields, and the geometrical structure of the underlying spacetime. This is directly analogous to the definition of the multiway causal graph, whose causal edges between branchlike-separated updating events encode the quantum mechanical structure of the multiway evolution graph, and whose causal edges between spacelike-separated updating events encode the relativistic structure of a pure (spacetime) causal graph.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory. The twistor correspondence, at least in Penrose&#8217;s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. <a href="#more" class="more chevron-after">Read more</a>"> Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory. The twistor correspondence, at least in Penrose’s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-16 00:00:00"> <p class="date">March 16, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-spin-networks-spin-foams-and-loop-quantum-gravity/">How do your models relate to spin networks, spin foams and loop quantum gravity?</a></h2> <div class="introtext" data-text="<p>One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, whilst a spin foam is a higher-dimensional version of the same idea, with the directed graph now replaced with a topological 2-complex, representing the overall quantum state of the entire four-dimensional spacetime. In this way, spin networks and spin foams may be thought of as being directly analogous to spatial hypergraphs and (multiway) causal graphs for Wolfram model systems. However, the crucial distinction is that, in the case of spin networks, edges correspond explicitly to irreducible representations of some predefined compact Lie group (with vertices corresponding to the intertwiners of the adjacent representations), whereas the spatial hyperedges in the case of Wolfram model systems correspond to abstract relations between elementary elements, with no group structure explicitly defined (in other words, all salient algebraic and geometrical features of Wolfram model systems are purely emergent, as opposed to being &#8220;burned in&#8221; to the underlying combinatorial structure, as is the case in spin networks and spin foams).</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, <a href="#more" class="more chevron-after">Read more</a>"> One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-16 12:38:40"> <p class="date">March 16, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-tensor-networks/">How do your models relate to tensor networks?</a></h2> <div class="introtext" data-text="<p>Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, connections between branchlike states denote entanglements between global multiway states within our models. However, unlike with a tensor network, the model specifies explicitly how these branchlike hypersurfaces evolve, in accordance with some multiway analog of the Einstein field equations (with, for instance, the Fubini–Study metric tensor playing the role of the standard spacetime metric tensor).</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, <a href="#more" class="more chevron-after">Read more</a>"> Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-17 00:00:00"> <p class="date">March 17, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-causal-set-theory-and-causal-dynamical-triangulation/">How do your models relate to causal set theory and causal dynamical triangulation?</a></h2> <div class="introtext" data-text="<p>Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, antisymmetry, transitivity (by virtue of the analog with the causal structure of a Lorentzian manifold), and local finiteness (by virtue of the discrete nature of the events), just as in a standard causal set. The formal structure of the Wolfram model may, in fact, be thought of as being an abstract generalization of a causal dynamical triangulation, in which spacetime is triangulated topologically into a simplicial complex of &#8220;pentachora&#8221; (4-simplices), which evolve in accordance with some deterministic dynamical law; the only difference in our case is that the choice of simplex is less constrained, because our formulation in terms of hypergraphs is more topologically generic.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, <a href="#more" class="more chevron-after">Read more</a>"> Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> <div class="project relations-to-other-approaches" data-position="normal" data-date="2020-03-18 00:00:00"> <p class="date">March 18, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/relations-to-other-approaches/how-do-your-models-relate-to-string-theory/">How do your models relate to string theory?</a></h2> <div class="introtext" data-text="<p>The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as &#8220;snake states&#8221;—sets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, their linear superposition itself corresponds to a valid global state), with distinct snake states thus being purely branchlike-separated. The worldsheet (or, more generally, worldvolume) defined by the trajectory of a snake state through the multiway system is therefore some higher-dimensional analog of the worldline defined by the trajectory of an individual multiway eigenstate. The convergence and divergence of branch pairs in the multiway system can hence be described purely in terms of splitting and joining operations on these worldsheets, which we conjecture may be related to the splitting and joining vertices for propagators in, for instance, light-cone string field theory.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as &#8220;snake states&#8221;—sets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, <a href="#more" class="more chevron-after">Read more</a>"> The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as “snake states”鈥攕ets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="relations-to-other-approaches" href="https://www.wolframphysics.org/questions/relations-to-other-approaches">(3) Relations to Other Approaches</a> </div> </div> </div> </div> <footer id="footer"> <div class="inner"></div> </footer> <script src="https://www.wolframphysics.org/questions/wp-content/themes/physics-questions/js/scripts.js"></script> <script src="/common/templates/www.wolframphysics.org/js/global.js.en"></script> </main> <footer id="footer"> <div id="introduction-pad" class="hide"></div> <div class="inner cf"> <ul class="footer-community"> <li><a href="//community.wolfram.com/content?curTag=wolfram%20fundamental%20physics%20project">Discussion Forum</a></li> <li><a href="/education-collaboration/">Education & Collaboration Opportunities</a></li> </ul> <ul class="footer-contact"> <li><a target="_blank" href="//x.com/stephen_wolfram/">X</a></li> <li><a target="_blank" href="//www.facebook.com/Stephen-Wolfram-188916357807416/">Facebook</a></li> <li><a target="_blank" href="//www.linkedin.com/in/stephenwolfram">LinkedIn</a></li> <li><a target="_blank" href="//www.instagram.com/stephenwolfram/">Instagram</a></li> <li><a href="/contact/">Contact</a></li> </ul> </div> </footer>  <div id ="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script>  </body> </html>

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The Wolfram Physics Project Q&A : (3) Relations to Other Approaches