The Wolfram Physics Project: Q&A

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href="/archives/index/">Archives</a></li> </ul> </nav> </header><main class="main"> <header class="main-header"> <div class="inner"> <div class="medium-col-width"> <a class="breadcrumb" href="https://www.wolframphysics.org/questions/">See all questions</a> <h1 class="heading">Wolfram Physics Q&A</h1> <div class="tagline cf"> <a href="/questions/ask-a-question" class="button float-r submit-a-question"> <svg width="24px" height="24px" viewBox="0 0 24 24"> <g id="qa-inline" stroke="none" stroke-width="1" fill="none" fill-rule="evenodd"> <path d="M20,3.5 L4,3.5 C3.58578644,3.5 3.21078644,3.66789322 2.93933983,3.93933983 C2.66789322,4.21078644 2.5,4.58578644 2.5,5 L2.5,15 C2.5,15.4142136 2.66789322,15.7892136 2.93933983,16.0606602 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 on" 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" 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">All</h1><span id="count">(49)</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 scientific-general-interest" data-position="normal" data-date="2020-02-27 19:25:15"> <p class="date">February 27, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/how-do-your-models-relate-to-the-anthropic-principle/">How do your models relate to the anthropic principle?</a></h2> <div class="introtext" data-text="<p><span data-expression="RowBox[{&quot;The&quot;, &quot; &quot;, &quot;anthropic&quot;, &quot; &quot;, &quot;principle&quot;, &quot; &quot;, &quot;main&quot;, &quot; &quot;, &quot;thrust&quot;, &quot; &quot;, &quot;is&quot;, &quot; &quot;, &quot;to&quot;, &quot; &quot;, &quot;say&quot;, &quot; &quot;, &quot;that&quot;, &quot; &quot;, &quot;for&quot;, &quot; &quot;, &quot;life&quot;, &quot;/&quot;, &quot;intelligence&quot;, &quot;/&quot;, &quot;observers&quot;, &quot; &quot;, &quot;to&quot;, &quot; &quot;, &quot;exist&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;the&quot;, &quot; &quot;, &quot;universe&quot;, &quot; &quot;, &quot;must&quot;, &quot; &quot;, &quot;be&quot;, &quot; &quot;, &quot;a&quot;, &quot; &quot;, &quot;certain&quot;, &quot; &quot;, &quot;way&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;It&quot;, &quot; &quot;, &quot;is&quot;, &quot; &quot;, &quot;true&quot;, &quot; &quot;, &quot;that&quot;, &quot; &quot;, &quot;what&quot;, &quot; &quot;, &quot;our&quot;, &quot; &quot;, &quot;models&quot;, &quot; &quot;, &quot;suggest&quot;, &quot; &quot;, &quot;is&quot;, &quot; &quot;, &quot;that&quot;, &quot; &quot;, &quot;the&quot;, &quot; &quot;, &quot;universe&quot;, &quot; &quot;, &quot;looks&quot;, &quot; &quot;, &quot;the&quot;, &quot; &quot;, &quot;way&quot;, &quot; &quot;, &quot;it&quot;, &quot; &quot;, &quot;does&quot;, &quot; &quot;, &quot;to&quot;, &quot; &quot;, &quot;us&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;because&quot;, &quot; &quot;, &quot;we&quot;, &quot; &quot;, &quot;are&quot;, &quot; &quot;, &quot;a&quot;, &quot; &quot;, &quot;certain&quot;, &quot; &quot;, &quot;way&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;The&quot;, &quot; &quot;, &quot;anthropic&quot;, &quot; &quot;, &quot;principle&quot;, &quot; &quot;, &quot;would&quot;, &quot; &quot;, &quot;say&quot;, &quot; &quot;, &quot;that&quot;, &quot; &quot;, &quot;we&quot;, &quot; &quot;, &quot;couldn't&quot;, &quot; &quot;, &quot;exist&quot;, StyleBox[RowBox[{&quot; &quot;, &quot;(&quot;}]], &quot;in&quot;, &quot; &quot;, &quot;any&quot;, &quot; &quot;, &quot;way&quot;, StyleBox[RowBox[{&quot;)&quot;, &quot; &quot;}]], &quot;unless&quot;, &quot; &quot;, &quot;the&quot;, &quot; &quot;, &quot;universe&quot;, &quot; &quot;, &quot;was&quot;, &quot; &quot;, &quot;a&quot;, &quot; &quot;, &quot;certain&quot;, &quot; &quot;, &quot;way&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;But&quot;, &quot; &quot;, &quot;our&quot;, &quot; &quot;, &quot;models&quot;, &quot; &quot;, &quot;say&quot;, &quot; &quot;, &quot;that&quot;, &quot; &quot;, &quot;we&quot;, &quot; &quot;, &quot;can&quot;, &quot; &quot;, &quot;exist&quot;, &quot; &quot;, &quot;in&quot;, &quot; &quot;, &quot;many&quot;, &quot; &quot;, &quot;ways&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;but&quot;, &quot; &quot;, &quot;the&quot;, &quot; &quot;, &quot;way&quot;, &quot; &quot;, &quot;we&quot;, &quot; &quot;, &quot;perceive&quot;, &quot; &quot;, &quot;the&quot;, &quot; &quot;, &quot;same&quot;, &quot; &quot;, &quot;underlying&quot;, &quot; &quot;, &quot;universe&quot;, &quot; &quot;, &quot;would&quot;, &quot; &quot;, &quot;depend&quot;, &quot; &quot;, &quot;on&quot;, &quot; &quot;, &quot;our&quot;, &quot; &quot;, &quot;details&quot;, &quot;.&quot;}]">The anthropic principle main thrust is to say that for life/intelligence/observers to exist, the universe must be a certain way. It is true that what our models suggest is that the universe looks the way it does to us, because we are a certain way. The anthropic principle would say that we couldn&#8217;t exist (in any way) unless the universe was a certain way. But our models say that we can exist in many ways, but the way we perceive the same underlying universe would depend on our details.</span></p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The anthropic principle main thrust is to say that for life/intelligence/observers to exist, the universe must be a certain way. It is true that what our models suggest is that the universe looks the way it does to us, because we are a certain way. The anthropic principle would say that we couldn&#8217;t exist (in any way) unless the universe was a certain way. <a href="#more" class="more chevron-after">Read more</a>"> The anthropic principle main thrust is to say that for life/intelligence/observers to exist, the universe must be a certain way. It is true that what our models suggest is that the universe looks the way it does to us, because we are a certain way. The anthropic principle would say that we couldn’t exist (in any way) unless the universe was a certain way. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project quantum-mechanics computation-theory" data-position="normal" data-date="2020-03-05 00:00:00"> <p class="date">March 5, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-does-quantum-computation-work-within-the-context-of-your-models/">How does quantum computation work within the context of your models?</a></h2> <div class="introtext" data-text="<p>In a surprisingly clean way! In short, one straightforward consequence of our interpretation of quantum mechanics in terms of multiway evolutions is the following, very concrete, interpretation of the relationship between Turing machines, non-deterministic Turing machines, and quantum Turing machines: classical Turing machines evolve along a single path of the multiway system (using a deterministic rule to select which branches to follow), non-deterministic Turing machines also evolve along single paths (but now using a non-deterministic rule to select the sequence of successive branches to take), and quantum Turing machines evolve across the entire multiway system itself (i.e. along a superposition of all possible paths).</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="In a surprisingly clean way! In short, one straightforward consequence of our interpretation of quantum mechanics in terms of multiway evolutions is the following, very concrete, interpretation of the relationship between Turing machines, non-deterministic Turing machines, and quantum Turing machines: classical Turing machines evolve along a single path of the multiway system (using a deterministic rule to select which branches to follow), <a href="#more" class="more chevron-after">Read more</a>"> In a surprisingly clean way! In short, one straightforward consequence of our interpretation of quantum mechanics in terms of multiway evolutions is the following, very concrete, interpretation of the relationship between Turing machines, non-deterministic Turing machines, and quantum Turing machines: classical Turing machines evolve along a single path of the multiway system (using a deterministic rule to select which branches to follow), <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <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 quantum-mechanics" data-position="normal" data-date="2020-03-06 00:00:00"> <p class="date">March 6, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-does-wave-particle-duality-work-in-your-models/">How does wave-particle duality work in your models?</a></h2> <div class="introtext" data-text="<p>Much like Bell&#8217;s theorem, the phenomenon of wave-particle duality follows immediately from the basic combinatorial properties of the multiway causal graph.</p> <p>A geodesic bundle propagating through an ordinary (i.e. purely relativistic) causal graph can be thought of as corresponding to the trajectory of a collection of test particles. On the other hand, a geodesic bundle propagating through a pure multiway evolution graph can be thought of as corresponding to the trajectory of a quantum wave packet (since each branch of the multiway evolution graph is analogous to the evolution history of a single quantum eigenstate, and therefore a collection of multiway branches corresponds to the evolution history of some linear superposition of those eigenstates).</p> <p>Since the multiway causal graph reflects both the structure of the multiway evolution graph and the structure of all of its associated causal graphs, any valid foliation of the multiway causal graph will consist of a time-ordered sequence of hypersurfaces, each of which will contain pairs of updating events that can be either spacelike-separated, branchlike-separated, or some combination of the two, with the type of separation depending upon the particular choice of foliation. Therefore, an observer who is embedded within a particular multiway causal foliation will, in general, find it impossible to determine whether a geodesic bundle propagating through the multiway causal graph corresponds to the evolution of a collection of test particles, a wave packet, or both (since the geodesics themselves will either appear to be purely spacelike-separated, purely branchlike-separated, or a combination, depending on the observer). Thus, wave-particle duality is just one of many immediate consequences of the principle of multiway relativity—the preservation of timelike-orderings of updating events in the multiway causal graph, independent of the choice of foliation.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Much like Bell&#8217;s theorem, the phenomenon of wave-particle duality follows immediately from the basic combinatorial properties of the multiway causal graph. A geodesic bundle propagating through an ordinary (i.e. purely relativistic) causal graph can be thought of as corresponding to the trajectory of a collection of test particles. On the other hand, <a href="#more" class="more chevron-after">Read more</a>"> Much like Bell’s theorem, the phenomenon of wave-particle duality follows immediately from the basic combinatorial properties of the multiway causal graph. A geodesic bundle propagating through an ordinary (i.e. purely relativistic) causal graph can be thought of as corresponding to the trajectory of a collection of test particles. On the other hand, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project spacetime-relativity" data-position="normal" data-date="2020-03-06 00:00:00"> <p class="date">March 6, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/spacetime-relativity/how-can-your-models-be-lorentz-invariant/">How can your models be Lorentz invariant?</a></h2> <div class="introtext" data-text="<p>Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, in the case of spatially flat hypersurfaces, to a possible inertial reference frame), and because each such foliation also defines a particular updating order for the underlying spatial hypergraph, the condition of causal invariance necessarily ensures that the orderings of timelike-separated updating events are always preserved across all inertial reference frames, even though the orderings of spacelike-separated updating events are not. This is precisely the statement of Lorentz covariance.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, <a href="#more" class="more chevron-after">Read more</a>"> Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> </div> </div> <div class="project spacetime-relativity" data-position="normal" data-date="2020-03-07 00:00:00"> <p class="date">March 7, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/spacetime-relativity/how-do-black-holes-work-within-the-context-of-your-models/">How do black holes work within the context of your models?</a></h2> <div class="introtext" data-text="<p>Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is &#8220;causally disconnected&#8221; from the latter region (analogous to the definition of an apparent horizon in spacetime as being the region from which light rays cannot escape to future null infinity). If the disconnection is symmetric (i.e. if region 1 and region 2 are mutually unreachable), then this is analogous to a cosmological event horizon. On the other hand, if the disconnection is asymmetric (i.e. if region 1 is reachable from region 2, but not vice versa, which occurs whenever all causal edges connecting the two regions are oriented strictly in the direction of region 1), then this is analogous to a black hole event horizon.</p> <p>The analog of a gravitational singularity is a spatially localized but temporally extended structure in the causal graph with an unusually high density of causal edges. For certain classes of rules, spatially localized structures with sufficiently high causal edge density necessarily break off into locally disconnected regions of the causal graph; as such, these rules can be thought of as being consistent with Penrose&#8217;s weak cosmic censorship hypothesis.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is &#8220;causally disconnected&#8221; <a href="#more" class="more chevron-after">Read more</a>"> Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is “causally disconnected” <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-07 09:43:15"> <p class="date">March 7, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-do-your-models-relate-to-the-de-broglie-bohmpilot-wave-formulation-of-quantum-mechanics/">How do your models relate to the de Broglie–Bohm/pilot wave formulation of quantum mechanics?</a></h2> <div class="introtext" data-text="<p>Our proof of the violation of the CHSH inequality for our model works in much the same way as it does for other standard deterministic and nonlocal interpretations of quantum mechanics, such as the de Broglie&ndash;Bohm (otherwise known as the pilot wave or causal) interpretation. However, in our particular case, this nonlocality does not emerge from the propagation of a pilot wave or similar structure, but rather results from the structure of the multiway causal graph (since it allows for the existence of causal connections between branchlike-local microstates in the multiway system, which may or may not be spacelike-local).</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Our proof of the violation of the CHSH inequality for our model works in much the same way as it does for other standard deterministic and nonlocal interpretations of quantum mechanics, such as the de Broglie&ndash;Bohm (otherwise known as the pilot wave or causal) interpretation. However, in our particular case, this nonlocality does not emerge from the propagation of a pilot wave or similar structure, <a href="#more" class="more chevron-after">Read more</a>"> Our proof of the violation of the CHSH inequality for our model works in much the same way as it does for other standard deterministic and nonlocal interpretations of quantum mechanics, such as the de Broglie–Bohm (otherwise known as the pilot wave or causal) interpretation. However, in our particular case, this nonlocality does not emerge from the propagation of a pilot wave or similar structure, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-07 10:41:55"> <p class="date">March 7, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-does-quantum-interference-occur-within-your-models/">How does quantum interference occur within your models?</a></h2> <div class="introtext" data-text="<p>Interference occurs as a natural byproduct of the Knuth–Bendix completion procedure for multiway evolution graphs. The simplest way this can work, in the case of the double slit experiment, is as follows: in one multiway branch, the photon goes through one slit, and in another multiway branch, the photon goes through the other slit. By applying a Knuth–Bendix completion, one introduces effective lemmas that equate the divergent branch pair states between these two branches; these lemmas are sufficiently general that they allow for new states in the multiway evolution graph to be reached, and these correspond exactly to the interference states in which the photon traveled through both slits and interfered with itself.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Interference occurs as a natural byproduct of the Knuth–Bendix completion procedure for multiway evolution graphs. The simplest way this can work, in the case of the double slit experiment, is as follows: in one multiway branch, the photon goes through one slit, and in another multiway branch, the photon goes through the other slit. <a href="#more" class="more chevron-after">Read more</a>"> Interference occurs as a natural byproduct of the Knuth–Bendix completion procedure for multiway evolution graphs. The simplest way this can work, in the case of the double slit experiment, is as follows: in one multiway branch, the photon goes through one slit, and in another multiway branch, the photon goes through the other slit. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-07 12:40:41"> <p class="date">March 7, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-do-your-models-relate-to-the-many-worlds-formulation-of-quantum-mechanics/">How do your models relate to the many-worlds formulation of quantum mechanics?</a></h2> <div class="introtext" data-text="<p>The simplest variant of the (Everettian) many-worlds interpretation of quantum mechanics, in which there is no effective interference between distinct branches of history, may be thought of as corresponding to the special case of multiway evolution in which there is no resolution of branch pairs (i.e. there is only branch pair divergence), and in which the observer follows only a single multiway branch. The full version of our model, with branch pair convergence and measurement-imposed completion procedures (as detailed in the question on interference), may therefore be thought of as corresponding to a version of Deutsch&#8217;s variant of the many-worlds interpretation, in which branches of history are permitted to interfere.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The simplest variant of the (Everettian) many-worlds interpretation of quantum mechanics, in which there is no effective interference between distinct branches of history, may be thought of as corresponding to the special case of multiway evolution in which there is no resolution of branch pairs (i.e. there is only branch pair divergence), <a href="#more" class="more chevron-after">Read more</a>"> The simplest variant of the (Everettian) many-worlds interpretation of quantum mechanics, in which there is no effective interference between distinct branches of history, may be thought of as corresponding to the special case of multiway evolution in which there is no resolution of branch pairs (i.e. there is only branch pair divergence), <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-07 20:29:16"> <p class="date">March 7, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-can-your-models-be-consistent-with-bells-theorem/">How can your models be consistent with Bell’s theorem?</a></h2> <div class="introtext" data-text="<p>Despite the deterministic nature of the Wolfram model, consistency with Bell&#8217;s theorem is actually a very natural consequence of the combinatorial structure of the multiway causal graph. By allowing for the existence of causal connections not only between updating events on the same branch of evolutionary history, but also between updating events on distinct branches of evolution history, one immediately obtains an explicitly nonlocal theory of multiway evolution. More precisely, one extends the notion of causal locality beyond mere spatial locality, since events that are branchlike-local will not, in general, also be spacelike-local. Therefore, one is able to prove violation of the Bell-CHSH inequality in much the same way as one does for standard deterministic and nonlocal interpretations of quantum mechanics, such as the de Broglie&ndash;Bohm or causal interpretation.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Despite the deterministic nature of the Wolfram model, consistency with Bell&#8217;s theorem is actually a very natural consequence of the combinatorial structure of the multiway causal graph. By allowing for the existence of causal connections not only between updating events on the same branch of evolutionary history, but also between updating events on distinct branches of evolution history, <a href="#more" class="more chevron-after">Read more</a>"> Despite the deterministic nature of the Wolfram model, consistency with Bell’s theorem is actually a very natural consequence of the combinatorial structure of the multiway causal graph. By allowing for the existence of causal connections not only between updating events on the same branch of evolutionary history, but also between updating events on distinct branches of evolution history, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-08 00:00:00"> <p class="date">March 8, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-does-quantum-entanglement-occur-in-your-models/">How does quantum entanglement occur in your models?</a></h2> <div class="introtext" data-text="<p>Two global Wolfram model states are said to be &#8220;entangled&#8221; if they share a common ancestor in the multiway evolution graph. Since spacelike-locality is not a necessary condition for branchlike-locality, it is possible for these states to be causally connected (i.e. to be connected in the multiway causal graph) even if they are not spatially local. This is the essence of quantum entanglement as it occurs, for instance, in the context of Bell&#8217;s theorem.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Two global Wolfram model states are said to be &#8220;entangled&#8221; if they share a common ancestor in the multiway evolution graph. Since spacelike-locality is not a necessary condition for branchlike-locality, it is possible for these states to be causally connected (i.e. to be connected in the multiway causal graph) even if they are not spatially local. <a href="#more" class="more chevron-after">Read more</a>"> Two global Wolfram model states are said to be “entangled” if they share a common ancestor in the multiway evolution graph. Since spacelike-locality is not a necessary condition for branchlike-locality, it is possible for these states to be causally connected (i.e. to be connected in the multiway causal graph) even if they are not spatially local. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project quantum-mechanics" data-position="normal" data-date="2020-03-09 00:00:00"> <p class="date">March 9, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/quantum-mechanics/how-does-the-uncertainty-principle-work-in-your-models/">How does the uncertainty principle work in your models?</a></h2> <div class="introtext" data-text="<p>One particularly exciting feature of the Wolfram model is that its basic structure allows us to prove many deep quantum mechanical results, such as the uncertainty principle, as pure theorems about abstract term rewriting systems.</p> <p>One begins by noting that a pair of abstract rewrite relations, R1 and R2, are said to &#8220;commute&#8221; if the state obtained by applying R1 and then R2 is identical to the state obtained by applying R2 and then R1. If a multiway Wolfram model evolution is not confluent, in the sense that there exist bifurcations in the multiway evolution graph that never re-converge, then this immediately implies the existence of non-commutative rewrite relations (since an abstract rewriting system is confluent if and only if it commutes with itself). Since each updating event in the multiway system can be thought of as being the application of an abstract rewrite relation, it follows that there must exist pairs of updating events that do not commute, in the sense that the final hypergraph obtained will depend upon the timelike-ordering of the application of those events.</p> <p>If we now interpret the multiway system as being the discrete analog of a (complex) projective Hilbert space, with the rewrite relations being linear operators acting on this space, then this statement immediately reduces to the statement of the standard uncertainty principle regarding the timelike-orderings of measurement operations for pairs of non-commuting observables in quantum mechanics.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="One particularly exciting feature of the Wolfram model is that its basic structure allows us to prove many deep quantum mechanical results, such as the uncertainty principle, as pure theorems about abstract term rewriting systems. One begins by noting that a pair of abstract rewrite relations, R1 and R2, are said to &#8220;commute&#8221; <a href="#more" class="more chevron-after">Read more</a>"> One particularly exciting feature of the Wolfram model is that its basic structure allows us to prove many deep quantum mechanical results, such as the uncertainty principle, as pure theorems about abstract term rewriting systems. One begins by noting that a pair of abstract rewrite relations, R1 and R2, are said to “commute” <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="quantum-mechanics" href="https://www.wolframphysics.org/questions/quantum-mechanics">(5) Quantum Mechanics</a> </div> </div> <div class="project scientific-general-interest spacetime-relativity" data-position="normal" data-date="2020-03-09 18:52:23"> <p class="date">March 9, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/spacetime-relativity/do-your-models-permit-the-possibility-of-time-travel-i-e-the-existence-of-closed-timelike-curves/">Do your models permit the possibility of time travel (i.e. the existence of closed timelike curves)?</a></h2> <div class="introtext" data-text="<p>The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, and since the condition of causal invariance corresponds to the requirement that all paths in the multiway evolution graph yield causal graphs that are ultimately isomorphic, the existence of such a cycle clearly violates this property (since one could always make a causal graph that is &#8220;arbitrarily different&#8221; from all of the others, by simply traversing that cycle an arbitrary number of times). However, since we are open to the possibility that causal invariance may be violated over sufficiently short timescales (indeed, this appears to be critical to our derivation of quantum mechanics), the existence of short-lived (and presumably microscopic) CTCs is not ruled out by our formalism.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, <a href="#more" class="more chevron-after">Read more</a>"> The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> </div> </div> <div class="project spacetime-relativity" data-position="normal" data-date="2020-03-10 18:50:28"> <p class="date">March 10, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/spacetime-relativity/why-do-you-get-a-euclideanriemannian-metric-as-opposed-to-a-taxicab-metric-induced-on-your-hypergraphs/">Why do you get a Euclidean/Riemannian metric, as opposed to a taxicab metric, induced on your hypergraphs?</a></h2> <div class="introtext" data-text="<p>If one measures distances by considering lengths of single geodesics between pairs of points in a hypergraph, using (for instance) some variant of Dijkstra&#8217;s algorithm, then evidently the induced metric will be discrete, and akin to a generalized taxicab metric. However, our derivation of the Einstein field equations involves first defining the Ollivier-Ricci curvature, which works by considering finite &#8220;bundles&#8221; of such geodesics (where, for two points in the hypergraph, one constructs a pair of geodesic balls surrounding those points by considering collections of random walks, and then one determines the geodesic distances between corresponding points on those balls using the Wasserstein transportation metric between the balls, considered as probability measures). This has the consequence of effectively &#8220;softening&#8221; the natural combinatorial metric on the hypergraph into an appropriately discretized version of a Riemannian metric; the full details are given in our formal discussion of general relativity.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="If one measures distances by considering lengths of single geodesics between pairs of points in a hypergraph, using (for instance) some variant of Dijkstra&#8217;s algorithm, then evidently the induced metric will be discrete, and akin to a generalized taxicab metric. However, our derivation of the Einstein field equations involves first defining the Ollivier-Ricci curvature, <a href="#more" class="more chevron-after">Read more</a>"> If one measures distances by considering lengths of single geodesics between pairs of points in a hypergraph, using (for instance) some variant of Dijkstra’s algorithm, then evidently the induced metric will be discrete, and akin to a generalized taxicab metric. However, our derivation of the Einstein field equations involves first defining the Ollivier-Ricci curvature, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> </div> </div> <div class="project spacetime-relativity" data-position="normal" data-date="2020-03-11 00:00:00"> <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/spacetime-relativity/what-do-your-models-imply-regarding-dark-energy-and-the-cosmological-constant/">What do your models imply regarding dark energy and the cosmological constant?</a></h2> <div class="introtext" data-text="<p>Our derivation of general relativity in the continuum limit of Wolfram model systems that satisfy causal invariance and asymptotic dimensionality preservation defines the Einstein field equations only up to an integration constant, thus implying that the model is compatible with both zero and non-zero values of the cosmological constant. Since the energy-momentum tensor for a Wolfram model evolution corresponds to a measure of the flux of causal edges through certain discrete hypersurfaces in the causal graph, we can conclude that those causal edges that are associated with the evolution of elementary particles (such as, for instance, causal edges corresponding to the evolution of nonplanar regions of the spatial hypergraph) will correspond to standard (baryonic) matter contributions, and all remaining causal edges, that are simply associated with the evolution of the background hypergraph, will correspond to vacuum energy contributions. As the latter quantity may vary dynamically as a function of position within the causal graph, we can conclude that the Wolfram model is also compatible with dynamical scalar field models of dark energy, such as quintessence and moduli fields.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Our derivation of general relativity in the continuum limit of Wolfram model systems that satisfy causal invariance and asymptotic dimensionality preservation defines the Einstein field equations only up to an integration constant, thus implying that the model is compatible with both zero and non-zero values of the cosmological constant. Since the energy-momentum tensor for a Wolfram model evolution corresponds to a measure of the flux of causal edges through certain discrete hypersurfaces in the causal graph, <a href="#more" class="more chevron-after">Read more</a>"> Our derivation of general relativity in the continuum limit of Wolfram model systems that satisfy causal invariance and asymptotic dimensionality preservation defines the Einstein field equations only up to an integration constant, thus implying that the model is compatible with both zero and non-zero values of the cosmological constant. Since the energy-momentum tensor for a Wolfram model evolution corresponds to a measure of the flux of causal edges through certain discrete hypersurfaces in the causal graph, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</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 spacetime-relativity" data-position="normal" data-date="2020-03-12 00:00:00"> <p class="date">March 12, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/spacetime-relativity/are-your-models-consistent-with-inflationary-cosmology/">Are your models consistent with inflationary cosmology?</a></h2> <div class="introtext" data-text="<p>Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. Therefore, if the initial condition for the universe is a spatial hypergraph with abnormally high vertex connectivity (e.g. a complete graph), then we can interpret this as corresponding to an arbitrarily large number of initial spatial dimensions. If the update rules exhibit the property of being asymptotically dimensionality preserving, then they will eventually cause the effective dimensionality of space to converge to some fixed, finite value.</p> <p>Thinking about such a universe from the point of view of its causal structure, we can see that it therefore starts off with an arbitrarily large value for the speed of light (since the causal graph is arbitrarily densely connected, allowing information propagation at abnormally high speeds), which then converges down to a much lower value at late times. This makes such a universe compatible with a so-called “VSL” or “variable speed of light” cosmology; VSL cosmologies are known to yield similar observational consequences to standard inflationary models, and, in particular, allow for valid solutions to the horizon and flatness problems of <span class="special-character CapitalLambda">&#923;</span>CDM cosmology.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. <a href="#more" class="more chevron-after">Read more</a>"> Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="spacetime-relativity" href="https://www.wolframphysics.org/questions/spacetime-relativity">(4) Spacetime / Relativity</a> </div> </div> <div class="project computation-theory" data-position="normal" data-date="2020-03-12 19:04:30"> <p class="date">March 12, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/computation-theory/what-does-your-formalism-mean-for-computational-complexity-theory/">What does your formalism mean for computational complexity theory?</a></h2> <div class="introtext" data-text="<p>One very exciting side effect of our formalism is the ability to recast many open questions in theoretical computer science and computational complexity theory in terms of it; as an illustrative example of this, note that the P vs. NP problem can, at some level, be thought of as corresponding to a question about the relative rates of divergence and convergence of branch pairs in the multiway evolution graph for our universe.</p> <p>More precisely, we begin by noting that Turing machines compute by following a single multiway branch in a completely deterministic fashion. Nondeterministic Turing machines, on the other hand, compute by also following a single multiway branch, but with the choices of which successive branches to take made in accordance with some nondeterministic rule. Therefore, P vs. NP (i.e. the question of whether the set of all problems solvable in polynomial time by a deterministic Turing machine is identical to the set of problems solvable in polynomial time by a nondeterministic Turing machine) is ultimately a question about whether a multiway state obtained by following a predetermined path in the multiway system is always reachable by following a nondeterministic path of approximately the same length. This is trivially true in the case of highly causal-invariant universes (e.g. ones in which all multiway branches eventually converge to a normal form). For a more nontrivial, non-terminating multiway system, the relative rates of branch pair divergence/convergence place constraints on the degree to which P and NP can be related.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="One very exciting side effect of our formalism is the ability to recast many open questions in theoretical computer science and computational complexity theory in terms of it; as an illustrative example of this, note that the P vs. NP problem can, at some level, be thought of as corresponding to a question about the relative rates of divergence and convergence of branch pairs in the multiway evolution graph for our universe. <a href="#more" class="more chevron-after">Read more</a>"> One very exciting side effect of our formalism is the ability to recast many open questions in theoretical computer science and computational complexity theory in terms of it; as an illustrative example of this, note that the P vs. NP problem can, at some level, be thought of as corresponding to a question about the relative rates of divergence and convergence of branch pairs in the multiway evolution graph for our universe. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <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”—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> </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 scientific-general-interest" data-position="normal" data-date="2020-04-01 04:22:51"> <p class="date">April 1, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/is-this-a-theory-of-everything/">Is this a theory of everything?</a></h2> <div class="introtext" data-text="<p>It is intended to be an underlying theory of the whole universe, in perfect detail. If one could run the model long enough, then it is intended to reproduce everything about the universe, including the writing of this answer. However, the amount of computation required to do this would be immense&#8212;and the phenomenon of computational irreducibility implies that there cannot in general be shortcuts. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="It is intended to be an underlying theory of the whole universe, in perfect detail. If one could run the model long enough, then it is intended to reproduce everything about the universe, including the writing of this answer. However, the amount of computation required to do this would be immense&#8212;and the phenomenon of computational irreducibility implies that there cannot in general be shortcuts."> It is intended to be an underlying theory of the whole universe, in perfect detail. If one could run the model long enough, then it is intended to reproduce everything about the universe, including the writing of this answer. However, the amount of computation required to do this would be immense—and the phenomenon of computational irreducibility implies that there cannot in general be shortcuts. </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-01 05:21:25"> <p class="date">April 1, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/are-you-saying-that-the-universe-is-a-cellular-automaton/">Are you saying that the universe is a cellular automaton?</a></h2> <div class="introtext" data-text="<p>No. Cellular automata are very useful models for many things, and provided the intuition that led to the development of this model. But cellular automata as such have rigid predefined notions of space and time, and a critical feature of our models is that space and time are instead dynamic and emergent. Structurally, our models involve rewrite rules for collections or relations, or equivalently, for hypergraphs, rather than updates of values in pre-existing arrays of cells.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="No. Cellular automata are very useful models for many things, and provided the intuition that led to the development of this model. But cellular automata as such have rigid predefined notions of space and time, and a critical feature of our models is that space and time are instead dynamic and emergent. <a href="#more" class="more chevron-after">Read more</a>"> No. Cellular automata are very useful models for many things, and provided the intuition that led to the development of this model. But cellular automata as such have rigid predefined notions of space and time, and a critical feature of our models is that space and time are instead dynamic and emergent. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-02 05:20:04"> <p class="date">April 2, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/could-the-universe-just-stop/">Could the universe just stop?</a></h2> <div class="introtext" data-text="<p>Yes, in principle the rules for the universe could simply no longer apply to any part of the spatial hypergraph. If this situation occurred, it would mean that time would no longer progress, and the universe would reach a final state, or fixed point, in effect giving the final result of the computation that corresponded to its evolution. Given that the universe probably has 10<sup>300</sup> or more elements, behaving in a computationally irreducible way, it seems absolutely inconceivable that everything could effectively &#8220;line up&#8221; to reach a fixed point. If this were to happen, however, then it would imply that the evolution of the universe could be summarized with much less computational effort than actually doing the evolution, or, in other words, that the universe is not ultimately capable of full universal computation.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Yes, in principle the rules for the universe could simply no longer apply to any part of the spatial hypergraph. If this situation occurred, it would mean that time would no longer progress, and the universe would reach a final state, or fixed point, in effect giving the final result of the computation that corresponded to its evolution. <a href="#more" class="more chevron-after">Read more</a>"> Yes, in principle the rules for the universe could simply no longer apply to any part of the spatial hypergraph. If this situation occurred, it would mean that time would no longer progress, and the universe would reach a final state, or fixed point, in effect giving the final result of the computation that corresponded to its evolution. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-03 05:18:43"> <p class="date">April 3, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/could-there-be-more-than-one-correct-rule/">Could there be more than one correct rule?</a></h2> <div class="introtext" data-text="<p>Yes, the concept of rule space relativity suggests that many rules can be equivalent, but each different rule will be appropriate for a different &#8220;observer&#8221;, or, more specifically, will be the rule suitable for an observer using a certain language to describe the universe. Our particular description language&#8212;based on our sensory experience, and the formal descriptions of existing physics&#8212;may well have enough freedom that it allows several possible consistent rules.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Yes, the concept of rule space relativity suggests that many rules can be equivalent, but each different rule will be appropriate for a different &#8220;observer&#8221;, or, more specifically, will be the rule suitable for an observer using a certain language to describe the universe. Our particular description language&#8212;based on our sensory experience, <a href="#more" class="more chevron-after">Read more</a>"> Yes, the concept of rule space relativity suggests that many rules can be equivalent, but each different rule will be appropriate for a different “observer”, or, more specifically, will be the rule suitable for an observer using a certain language to describe the universe. Our particular description language—based on our sensory experience, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-04 05:14:37"> <p class="date">April 4, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/how-will-you-know-if-you-have-the-correct-rule/">How will you know if you have the correct rule?</a></h2> <div class="introtext" data-text="<p>Computational irreducibility means that it may be irreducibly difficult to determine any particular consequence of a rule. However, there is reason to hope that certain properties will be identifiable. If the rule is simple, then it is to be expected that just getting a few specifics of our universe exactly correct will be sufficient to determine the particular rule. For example, knowing that the universe has (at least roughly) three spatial dimensions, or knowing local gauge symmetry groups, will presumably already go far in homing in on the correct rule. Finding specific masses and properties of elementary particles will be a critical validation for any particular rule. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Computational irreducibility means that it may be irreducibly difficult to determine any particular consequence of a rule. However, there is reason to hope that certain properties will be identifiable. If the rule is simple, then it is to be expected that just getting a few specifics of our universe exactly correct will be sufficient to determine the particular rule. <a href="#more" class="more chevron-after">Read more</a>"> Computational irreducibility means that it may be irreducibly difficult to determine any particular consequence of a rule. However, there is reason to hope that certain properties will be identifiable. If the rule is simple, then it is to be expected that just getting a few specifics of our universe exactly correct will be sufficient to determine the particular rule. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-05 05:06:45"> <p class="date">April 5, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/what-does-your-model-say-about-the-simulation-argument/">What does your model say about the simulation argument?</a></h2> <div class="introtext" data-text="<p>The model implies that there is a definite computational rule that determines every aspect of what happens in our universe. If the universe is to be considered a &#8220;simulation&#8221; this would suggest that the rule is being determined by something outside the system, and presumably in an &#8220;intentional&#8221; way. It is difficult enough to extend the notion of intentionality far beyond the specifics of what humans do, making it unrealistic to attribute it to something beyond even the universe. In addition, the concept of rule-space relativity implies that in a sense all possible rules are equivalent, at least to an appropriate observer, and therefore there would be nothing for an entity setting up the simulation to &#8220;intentionally decide&#8221;&#8212;since any rule they could choose would appear to be the same universe to observers embedded within it.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The model implies that there is a definite computational rule that determines every aspect of what happens in our universe. If the universe is to be considered a &#8220;simulation&#8221; this would suggest that the rule is being determined by something outside the system, and presumably in an &#8220;intentional&#8221; way. It is difficult enough to extend the notion of intentionality far beyond the specifics of what humans do, <a href="#more" class="more chevron-after">Read more</a>"> The model implies that there is a definite computational rule that determines every aspect of what happens in our universe. If the universe is to be considered a “simulation” this would suggest that the rule is being determined by something outside the system, and presumably in an “intentional” way. It is difficult enough to extend the notion of intentionality far beyond the specifics of what humans do, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-05 05:08:43"> <p class="date">April 5, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/are-there-other-universes/">Are there other universes?</a></h2> <div class="introtext" data-text="<p>In our model, many possible rules yield causally disconnected regions of spacetime, often corresponding to disconnecting parts of the spatial hypergraph. In addition, there can be disconnected regions of branchial space, corresponding to causally disconnected branches of quantum evolution. These kinds of non-communicating regions are still operating according to the same underlying rule. But rule-space relativity in our models suggests that even universes with different rules are equivalent to observers embedded within the universe, implying that there cannot meaningfully be &#8220;other universes&#8221; that somehow run in parallel to ours with different rules. There can be different forms of description for our universe that are incoherent with each other, but they are still describing the same universe. The only possibility in our model for &#8220;other universes&#8221; with fundamentally different rules is for these universes to perform computations at a higher level in the arithmetic hierarchy, i.e. hypercomputations. However, such universes would inevitably be disconnected from us, effectively separated by the analog of a cosmological event horizon.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="In our model, many possible rules yield causally disconnected regions of spacetime, often corresponding to disconnecting parts of the spatial hypergraph. In addition, there can be disconnected regions of branchial space, corresponding to causally disconnected branches of quantum evolution. These kinds of non-communicating regions are still operating according to the same underlying rule. <a href="#more" class="more chevron-after">Read more</a>"> In our model, many possible rules yield causally disconnected regions of spacetime, often corresponding to disconnecting parts of the spatial hypergraph. In addition, there can be disconnected regions of branchial space, corresponding to causally disconnected branches of quantum evolution. These kinds of non-communicating regions are still operating according to the same underlying rule. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-05 20:27:35"> <p class="date">April 5, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/how-could-your-model-be-proved-wrong/">How could your model be proved wrong?</a></h2> <div class="introtext" data-text="<p>Any particular rule could be proved wrong by disagreeing with observations, for example predicting particles that do not exist. But the overall framework of our models is something more general, and not as directly amenable to experimental falsification. Asking how to falsify our framework is similar to asking how one would prove that calculus could not be a model for physics. An obvious answer would be another model successfully providing a fundamental theory of physics, and being proved incompatible.</p> <p>There are, however, some structural features of our models which are unavoidable. One of them is the assertion that hypercomputation is not physically realizable. But quite how we&#8212;with human perception and actuation capabilities&#8212;could explicitly set up and interpret hypercomputation is quite unclear.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Any particular rule could be proved wrong by disagreeing with observations, for example predicting particles that do not exist. But the overall framework of our models is something more general, and not as directly amenable to experimental falsification. Asking how to falsify our framework is similar to asking how one would prove that calculus could not be a model for physics. <a href="#more" class="more chevron-after">Read more</a>"> Any particular rule could be proved wrong by disagreeing with observations, for example predicting particles that do not exist. But the overall framework of our models is something more general, and not as directly amenable to experimental falsification. Asking how to falsify our framework is similar to asking how one would prove that calculus could not be a model for physics. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-06 05:02:19"> <p class="date">April 6, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/if-the-universe-is-computational-what-computer-is-it-running-on/">If the universe is computational, what computer is it running on?</a></h2> <div class="introtext" data-text="<p>None. It is just following certain rules that we can think of as computational. There is no underlying &#8220;substrate&#8221;. The universe is just doing what it does, and we are describing it in terms of computation. When we think about Newton&#8217;s laws describing the motion of the Earth using equations, we are also imagining the equations describe what the Earth is doing, not that the Earth itself has a mechanism inside that is solving the equations as <a href='https://www.wolfram.com/mathematica/'>Mathematica</a> might.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="None. It is just following certain rules that we can think of as computational. There is no underlying &#8220;substrate&#8221;. The universe is just doing what it does, and we are describing it in terms of computation. When we think about Newton&#8217;s laws describing the motion of the Earth using equations, we are also imagining the equations describe what the Earth is doing, <a href="#more" class="more chevron-after">Read more</a>"> None. It is just following certain rules that we can think of as computational. There is no underlying “substrate”. The universe is just doing what it does, and we are describing it in terms of computation. When we think about Newton’s laws describing the motion of the Earth using equations, we are also imagining the equations describe what the Earth is doing, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-07 04:59:56"> <p class="date">April 7, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/are-you-saying-that-the-universe-is-a-computer/">Are you saying that the universe is a computer?</a></h2> <div class="introtext" data-text="<p>&#8220;Computational&#8221;, yes. Our model implies that the universe operates at the lowest level according to definite rules of the kind one could readily program on a computer. But when one says &#8220;is a computer&#8221; one often means that one imagines that something has been constructed for the purpose of being a computer. All our model does is to say that the operation of the universe can be described computationally, not that the universe was in any way &#8220;built to be a computer&#8221;.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="&#8220;Computational&#8221;, yes. Our model implies that the universe operates at the lowest level according to definite rules of the kind one could readily program on a computer. But when one says &#8220;is a computer&#8221; one often means that one imagines that something has been constructed for the purpose of being a computer. <a href="#more" class="more chevron-after">Read more</a>"> “Computational”, yes. Our model implies that the universe operates at the lowest level according to definite rules of the kind one could readily program on a computer. But when one says “is a computer” one often means that one imagines that something has been constructed for the purpose of being a computer. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-08 01:38:16"> <p class="date">April 8, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/can-i-get-the-code-to-run-your-models/">Can I get the code to run your models?</a></h2> <div class="introtext" data-text="<p>Yes! It&#8217;s set up to run immediately in any <a href='https://www.wolfram.com/language'>Wolfram Language</a> environment, including <a href='https://www.wolframcloud.com/'>the cloud</a> (i.e. through a web browser). See the <a href='https://www.wolframphysics.org/tools/'>Software Tools</a> page. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Yes! It&#8217;s set up to run immediately in any <a href='https://www.wolfram.com/language'>Wolfram Language</a> environment, including <a href='https://www.wolframcloud.com/'>the cloud</a> (i.e. through a web browser). See the <a href='https://www.wolframphysics.org/tools/'>Software Tools</a> page."> Yes! It’s set up to run immediately in any <a href='https://www.wolfram.com/language'>Wolfram Language</a> environment, including <a href='https://www.wolframcloud.com/'>the cloud</a> (i.e. through a web browser). See the <a href='https://www.wolframphysics.org/tools/'>Software Tools</a> page. </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-08 02:34:08"> <p class="date">April 8, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/i-have-my-own-theory-will-you-look-at-it/">I have my own theory; will you look at it?</a></h2> <div class="introtext" data-text="<p>We&#8217;ve got our hands full studying one theory, so unless your theory is directly connected to what we&#8217;re working on, we&#8217;re not realistically going to be able to look at it.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="We&#8217;ve got our hands full studying one theory, so unless your theory is directly connected to what we&#8217;re working on, we&#8217;re not realistically going to be able to look at it."> We’ve got our hands full studying one theory, so unless your theory is directly connected to what we’re working on, we’re not realistically going to be able to look at it. </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-08 03:30:13"> <p class="date">April 8, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/what-background-do-i-need-to-understand-what-youre-doing/">What background do I need to understand what you’re doing?</a></h2> <div class="introtext" data-text="<p>We&#8217;ve tried to make the general outline of what we&#8217;re doing as broadly accessible as possible. But since we are connecting with existing theoretical physics, understanding the technical details requires understanding technical details of existing theoretical physics, often at a research or advanced graduate level. Some aspects of the project do not specifically require physics knowledge, but often instead require knowledge of advanced mathematics or theoretical computer science. Nevertheless, as part of the project we hope to provide <a href='https://education.wolfram.com/summer/school/'>educational programs</a> and <a href='https://www.wolframphysics.org/tools/'>resources</a> which will allow a wide range of people to learn what is needed to understand many aspects of our project.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="We&#8217;ve tried to make the general outline of what we&#8217;re doing as broadly accessible as possible. But since we are connecting with existing theoretical physics, understanding the technical details requires understanding technical details of existing theoretical physics, often at a research or advanced graduate level. Some aspects of the project do not specifically require physics knowledge, <a href="#more" class="more chevron-after">Read more</a>"> We’ve tried to make the general outline of what we’re doing as broadly accessible as possible. But since we are connecting with existing theoretical physics, understanding the technical details requires understanding technical details of existing theoretical physics, often at a research or advanced graduate level. Some aspects of the project do not specifically require physics knowledge, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-08 04:27:34"> <p class="date">April 8, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/can-i-sponsor-or-donate-to-your-project/">Can I sponsor or donate to your project?</a></h2> <div class="introtext" data-text="<p>This project has so far been funded by Stephen Wolfram and Wolfram Research, and has used internal Wolfram Research compute resources. As the project scales up, there will be opportunities for additional sponsorship to support research fellows, educational activities, outreach, computation, etc. There are also opportunities to provide large-scale computation resources. We will be setting up programs for individual donations, both financial and computational. In addition, there will be <a href='https://www.wolframphysics.org/help/'>many opportunities for volunteers interested in the project</a>.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="This project has so far been funded by Stephen Wolfram and Wolfram Research, and has used internal Wolfram Research compute resources. As the project scales up, there will be opportunities for additional sponsorship to support research fellows, educational activities, outreach, computation, etc. There are also opportunities to provide large-scale computation resources. <a href="#more" class="more chevron-after">Read more</a>"> This project has so far been funded by Stephen Wolfram and Wolfram Research, and has used internal Wolfram Research compute resources. As the project scales up, there will be opportunities for additional sponsorship to support research fellows, educational activities, outreach, computation, etc. There are also opportunities to provide large-scale computation resources. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project scientific-general-interest" data-position="normal" data-date="2020-04-08 04:59:34"> <p class="date">April 8, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/scientific-general-interest/does-your-theory-make-predictions/">Does your theory make predictions?</a></h2> <div class="introtext" data-text="<p>Ultimately it should predict everything about the universe, although many of these predictions will be computational irreducibly difficult to work out in detail. However, even at this stage, there are a variety of surprisingly concrete directions for predictions. One issue is that we do not yet know the overall quantitative scale of the core phenomena (since we do not know for sure the elementary length for discrete distances in space). However, we can already see that there are general predictions about cosmology, astrophysics and quantum processes, especially related to black holes. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Ultimately it should predict everything about the universe, although many of these predictions will be computational irreducibly difficult to work out in detail. However, even at this stage, there are a variety of surprisingly concrete directions for predictions. One issue is that we do not yet know the overall quantitative scale of the core phenomena (since we do not know for sure the elementary length for discrete distances in space). <a href="#more" class="more chevron-after">Read more</a>"> Ultimately it should predict everything about the universe, although many of these predictions will be computational irreducibly difficult to work out in detail. However, even at this stage, there are a variety of surprisingly concrete directions for predictions. One issue is that we do not yet know the overall quantitative scale of the core phenomena (since we do not know for sure the elementary length for discrete distances in space). <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="scientific-general-interest" href="https://www.wolframphysics.org/questions/scientific-general-interest">(2) Scientific General Interest</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-08 05:24:36"> <p class="date">April 8, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/how-can-i-get-involved-in-your-project/">How can I get involved in your project?</a></h2> <div class="introtext" data-text="<p>We plan to make this a very open project, and <a href='https://www.wolframphysics.org/help/'>look forward to contributions from many people</a>. Core research contributions will typically require research-level education in theoretical physics, mathematics or certain areas of theoretical computer science, or sophisticated algorithmic programming. However, we will be <a href='https://www.wolframphysics.org/livestreams/'>livestreaming our working sessions</a>, and anyone can join the livestream and participate in the text chat. We will be organizing a variety of educational programs around the project, notably our <a href='https://education.wolfram.com/summer/school/'>Summer School</a>. We hope to expand our core team of researchers, as well as to have <a href='https://www.wolframphysics.org/contact/'>academic and other affiliates</a> associated with the project. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="We plan to make this a very open project, and <a href='https://www.wolframphysics.org/help/'>look forward to contributions from many people</a>. Core research contributions will typically require research-level education in theoretical physics, mathematics or certain areas of theoretical computer science, or sophisticated algorithmic programming. However, we will be <a href='https://www.wolframphysics.org/livestreams/'>livestreaming our working sessions</a>, <a href="#more" class="more chevron-after">Read more</a>"> We plan to make this a very open project, and <a href='https://www.wolframphysics.org/help/'>look forward to contributions from many people</a>. Core research contributions will typically require research-level education in theoretical physics, mathematics or certain areas of theoretical computer science, or sophisticated algorithmic programming. However, we will be <a href='https://www.wolframphysics.org/livestreams/'>livestreaming our working sessions</a>, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-09 04:55:31"> <p class="date">April 9, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/what-is-left-to-do-in-the-project/">What is left to do in the project?</a></h2> <div class="introtext" data-text="<p>A lot! We think we have identified the correct class of models and approach, but it remains to find specific rules and to connect them to all known aspects of physics, and to derive detailed experimental predictions, etc. In addition, we expect connections to many existing directions in physics and mathematics, and these remain to be elucidated in detail. Watch <a href='https://www.wolframphysics.org/livestreams/'>the livestreams</a> to see the process in action!</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="A lot! We think we have identified the correct class of models and approach, but it remains to find specific rules and to connect them to all known aspects of physics, and to derive detailed experimental predictions, etc. In addition, we expect connections to many existing directions in physics and mathematics, <a href="#more" class="more chevron-after">Read more</a>"> A lot! We think we have identified the correct class of models and approach, but it remains to find specific rules and to connect them to all known aspects of physics, and to derive detailed experimental predictions, etc. In addition, we expect connections to many existing directions in physics and mathematics, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-10 04:51:27"> <p class="date">April 10, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/have-you-found-the-rule-for-the-universe/">Have you found The Rule for the universe?</a></h2> <div class="introtext" data-text="<p>We believe we have found the class of rules, but (so far as we know) we have not yet found the specific rule. The phenomenon of computational irreducibility makes it difficult to determine the complete consequences of any given rule. However, a major finding of the project so far is that the core theories of current physics can be derived generically for models of the class we have identified, without needing to know the specific underlying rule. One of the more abstract findings of the project is that it is also the case that the specific rule to use to describe the universe depends on one&#8217;s language for description, and so with different description languages different rules will be considered The Rule.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="We believe we have found the class of rules, but (so far as we know) we have not yet found the specific rule. The phenomenon of computational irreducibility makes it difficult to determine the complete consequences of any given rule. However, a major finding of the project so far is that the core theories of current physics can be derived generically for models of the class we have identified, <a href="#more" class="more chevron-after">Read more</a>"> We believe we have found the class of rules, but (so far as we know) we have not yet found the specific rule. The phenomenon of computational irreducibility makes it difficult to determine the complete consequences of any given rule. However, a major finding of the project so far is that the core theories of current physics can be derived generically for models of the class we have identified, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-11 04:47:47"> <p class="date">April 11, 2020</p> <p class="asker"><em>Answered by: Stephen Wolfram</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/does-the-project-invalidate-existing-physics/">Does the project invalidate existing physics?</a></h2> <div class="introtext" data-text="<p>No. But it gives a coherent foundation for what previously appeared to be disparate ideas and results. In doing this, it introduces new concepts that are different from those in existing physics. For example, it suggests that space is fundamentally discrete, rather than continuous. It also suggests that time is fundamentally different from space rather than being just part of a combined spacetime. Despite such differences&#8212;which are primarily relevant on extremely small scales&#8212;existing physics emerges. In addition, our model appears to dovetail very elegantly with many recent formal directions in physics. (See <a href='https://www.wolframphysics.org/questions/relations-to-other-approaches'>Relations to Other Approaches</a>.)</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="No. But it gives a coherent foundation for what previously appeared to be disparate ideas and results. In doing this, it introduces new concepts that are different from those in existing physics. For example, it suggests that space is fundamentally discrete, rather than continuous. It also suggests that time is fundamentally different from space rather than being just part of a combined spacetime. <a href="#more" class="more chevron-after">Read more</a>"> No. But it gives a coherent foundation for what previously appeared to be disparate ideas and results. In doing this, it introduces new concepts that are different from those in existing physics. For example, it suggests that space is fundamentally discrete, rather than continuous. It also suggests that time is fundamentally different from space rather than being just part of a combined spacetime. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-12 04:42:00"> <p class="date">April 12, 2020</p> <p class="asker"><em>Answered by: Jonathan Gorard</em></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/what-existing-approaches-is-the-project-closest-to/">What existing approaches is the project closest to?</a></h2> <div class="introtext" data-text="<p>First and foremost (though it&#8217;s really an extension of the same project), Stephen Wolfram&#8217;s work from 2002 in <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. Other approaches that have definite similarities to certain aspects of our formalism include causal dynamical triangulation (which can be thought of as corresponding to a special case of our more topologically generic description of spacetime in terms of hypergraphs&#8212;namely the case in which spacetime is triangulated topologically into a simplicial complex of pentachora), loop quantum gravity (since Wolfram model evolutions can be thought of as corresponding to generalizations of spin foams in which spatial hyperedges are purely abstract, and, unlike in spin networks, do not have a compact Lie group structure explicitly defined), and twistor theory (the twistor correspondence space can be thought of as being a continuous model of the multiway causal graph, at least in certain idealized cases). The <a href='https://www.wolframphysics.org/questions/relations-to-other-approaches'>Relations to Other Approaches</a> section of this Q&#038;A gives more details. See also the <a href='https://www.wolframphysics.org/technical-introduction/notes-and-further-references'>Notes &#038; Further References</a> in <a href='https://www.wolframphysics.org/technical-introduction/'>Stephen Wolfram&#8217;s Technical Introduction</a>. </p> <a class='less' href='#close'>Close answer »</a>" data-truncate="First and foremost (though it&#8217;s really an extension of the same project), Stephen Wolfram&#8217;s work from 2002 in <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. Other approaches that have definite similarities to certain aspects of our formalism include causal dynamical triangulation (which can be thought of as corresponding to a special case of our more topologically generic description of spacetime in terms of hypergraphs&#8212;namely the case in which spacetime is triangulated topologically into a simplicial complex of pentachora), <a href="#more" class="more chevron-after">Read more</a>"> First and foremost (though it’s really an extension of the same project), Stephen Wolfram’s work from 2002 in <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. Other approaches that have definite similarities to certain aspects of our formalism include causal dynamical triangulation (which can be thought of as corresponding to a special case of our more topologically generic description of spacetime in terms of hypergraphs—namely the case in which spacetime is triangulated topologically into a simplicial complex of pentachora), <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-13 04:34:17"> <p class="date">April 13, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/what-is-the-history-and-background-to-the-project/">What is the history and background to the project?</a></h2> <div class="introtext" data-text="<p>It&#8217;s an outgrowth of Stephen Wolfram&#8217;s work in the 1990s, that led to the <a href='https://www.wolframscience.com/nks/chap-9--fundamental-physics/'>Fundamental Physics</a> section in his 2002 book <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. The project that it defined was long hibernated, but restarted in late 2019. The full story&#8212;going back to Stephen&#8217;s early life as a physicist&#8212;is in Stephen Wolfram&#8217;s post, &ldquo;<a href='https://writings.stephenwolfram.com/2020/04/how-we-got-here-the-backstory-of-the-wolfram-physics-project/'>How We Got Here: The Backstory of the Wolfram Physics Project</a>&rdquo;&#46;</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="It&#8217;s an outgrowth of Stephen Wolfram&#8217;s work in the 1990s, that led to the <a href='https://www.wolframscience.com/nks/chap-9--fundamental-physics/'>Fundamental Physics</a> section in his 2002 book <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. The project that it defined was long hibernated, but restarted in late 2019. The full story&#8212;going back to Stephen&#8217;s early life as a physicist&#8212;is in Stephen Wolfram&#8217;s post, <a href="#more" class="more chevron-after">Read more</a>"> It’s an outgrowth of Stephen Wolfram’s work in the 1990s, that led to the <a href='https://www.wolframscience.com/nks/chap-9--fundamental-physics/'>Fundamental Physics</a> section in his 2002 book <a href='https://www.wolframscience.com/nks/'><em>A New Kind of Science</em></a>. The project that it defined was long hibernated, but restarted in late 2019. The full story—going back to Stephen’s early life as a physicist—is in Stephen Wolfram’s post, <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-04-14 04:30:33"> <p class="date">April 14, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/what-is-the-quickest-way-to-understand-the-project/">What is the quickest way to understand the project?</a></h2> <div class="introtext" data-text="<p>It depends on your background. For a general reader, check out <a href='https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful'>Stephen Wolfram&#8217;s announcement</a>. For a more formal introduction, see <a href='https://www.wolframphysics.org/technical-introduction/'>Stephen Wolfram&#8217;s technical introduction</a>. Professional physicists may find it easiest to look at Jonathan Gorard&#8217;s papers on the derivations of <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-relativistic-and-gravitational-properties-of-the-wolfram-model.pdf'>relativity</a> and <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-quantum-mechanical-properties-of-the-wolfram-model.pdf'>quantum mechanics</a>. There&#8217;s also the <a href='https://www.wolframphysics.org/visual-summary/'>Visual Summary</a>, which gives a high-level overview. In addition, people who want to start doing their own computer experiments can check out the <a href='https://www.wolframcloud.com/obj/wolframphysics/Tools/hands-on-introduction-to-the-wolfram-physics-project.nb'>Hands-On Introduction</a>.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="It depends on your background. For a general reader, check out <a href='https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful'>Stephen Wolfram&#8217;s announcement</a>. For a more formal introduction, see <a href='https://www.wolframphysics.org/technical-introduction/'>Stephen Wolfram&#8217;s technical introduction</a>. Professional physicists may find it easiest to look at Jonathan Gorard&#8217;s papers on the derivations of <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-relativistic-and-gravitational-properties-of-the-wolfram-model.pdf'>relativity</a> and <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-quantum-mechanical-properties-of-the-wolfram-model.pdf'>quantum mechanics</a>. <a href="#more" class="more chevron-after">Read more</a>"> It depends on your background. For a general reader, check out <a href='https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful'>Stephen Wolfram’s announcement</a>. For a more formal introduction, see <a href='https://www.wolframphysics.org/technical-introduction/'>Stephen Wolfram’s technical introduction</a>. Professional physicists may find it easiest to look at Jonathan Gorard’s papers on the derivations of <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-relativistic-and-gravitational-properties-of-the-wolfram-model.pdf'>relativity</a> and <a href='https://www.wolframcloud.com/obj/wolframphysics/Documents/some-quantum-mechanical-properties-of-the-wolfram-model.pdf'>quantum mechanics</a>. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</a> </div> </div> <div class="project general" data-position="normal" data-date="2020-05-02 17:34:50"> <p class="date">May 2, 2020</p> <p class="asker"></p> <h2 class="projectname"><a href="https://www.wolframphysics.org/questions/general/has-the-project-been-peer-reviewed/">Has the project been peer reviewed?</a></h2> <div class="introtext" data-text="<p>The project is undergoing <a href='https://www.wolframphysics.org/peer-review/'>active, open post-publication peer review</a>, and is continually being refined and developed based on community input. Stephen Wolfram&#8217;s <a href='https://arxiv.org/abs/2004.08210' target='_blank'>core paper</a> is available on arXiv, and is intended for publication in an academic journal, as are <a href='https://www.wolframphysics.org/technical-documents/'>other project papers</a>. (See also comments <a href='https://writings.stephenwolfram.com/2020/04/the-wolfram-physics-project-the-first-two-weeks/#what-about-peer-review-and-all-that'>here</a>.)</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="The project is undergoing <a href='https://www.wolframphysics.org/peer-review/'>active, open post-publication peer review</a>, and is continually being refined and developed based on community input. Stephen Wolfram&#8217;s <a href='https://arxiv.org/abs/2004.08210' target='_blank'>core paper</a> is available on arXiv, and is intended for publication in an academic journal, as are <a href='https://www.wolframphysics.org/technical-documents/'>other project papers</a>. (See also comments <a href='https://writings.stephenwolfram.com/2020/04/the-wolfram-physics-project-the-first-two-weeks/#what-about-peer-review-and-all-that'>here</a>.)"> The project is undergoing <a href='https://www.wolframphysics.org/peer-review/'>active, open post-publication peer review</a>, and is continually being refined and developed based on community input. Stephen Wolfram’s <a href='https://arxiv.org/abs/2004.08210' target='_blank'>core paper</a> is available on arXiv, and is intended for publication in an academic journal, as are <a href='https://www.wolframphysics.org/technical-documents/'>other project papers</a>. (See also comments <a href='https://writings.stephenwolfram.com/2020/04/the-wolfram-physics-project-the-first-two-weeks/#what-about-peer-review-and-all-that'>here</a>.) </div> <div class="text"> <a class="tag" data-tag="general" href="https://www.wolframphysics.org/questions/general">(1) General</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