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Wolfram Physics Project: Working Session Wednesday, Apr. 29, 2020 [Finding Black Hole Structures]

Wolfram・167 minutes read

The physics project delves into black holes, exploring their structure, interior solutions, and unique features. Discussions range from causal connections in hypergraphs to the computational complexity of rule space, aiming to understand singularities and gravitational wave interactions better.

Insights

  • The physics project aims to explore black holes and their fine structure, focusing on uncovering significant findings during the three-week project period.
  • Stephen Hawking proposed a resolution to the black hole information paradox by suggesting apparent horizons instead of true event horizons, indicating that the loss of information in black holes may not lead to a loss of unitarity due to chaotic interior solutions.
  • Detection of event horizons in hypergraph systems can be achieved by plotting graph communities, potentially leading to the creation of causally disconnected observable universes.
  • The discussion involves understanding causal connections and event horizons through the analysis of future light cones and vertex components, emphasizing the need to establish causal connections by identifying common future light cones.
  • The study delves into computational complexity theory, exploring the computational complexity of rule space and its potential to inform geometries, concluding with reflections on spacetime singularities and the simulation of black holes through gravitational wave intersections.

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Recent questions

  • What is the primary focus of the physics project?

    The physics project aims to explore black holes and the fine structure within them. The goal is to uncover significant findings during the three-week project period, with a particular emphasis on the interior solutions of black holes that differ from the exterior solutions. The project also delves into the concept of event horizons and causal connections within hypergraph theory, seeking to understand the complexities of black holes and singularity structures.

  • How is the summer school adapting to current circumstances?

    The summer school, now in its 17th year, will be held as a remote digital experience for the first time, making it more accessible to a wider audience. The primary summer school is three weeks long, focusing on original projects in general Science and Technology, with a new fundamental physics track. A week zero will precede the three-week project time to provide foundational lectures, ensuring that participants are well-prepared for the in-depth exploration of topics like black holes and event horizons.

  • What new features have been added to enhance the physics project?

    The project has introduced a new Twitter stream, Wolfen physics, to provide detailed updates on live streams and project developments. Additionally, a forum has been added for open post-publication peer reviews for papers related to the project. The project is expanding its Q&A section on the website and enhancing the visual gallery with 3D geometries for potential 3D printing, offering participants a more interactive and engaging experience.

  • How are event horizons detected in hypergraph systems?

    Detecting event horizons in hypergraph systems can be done by plotting graph communities and analyzing the structure of the transition graph. The transition graph depicts which vertices can reach others, with one-way connections indicating black hole-like events. By analyzing future light cones and determining if points are causally connected based on their future interactions, researchers can identify common future light cones and vertex components to establish causal connections, shedding light on the presence of event horizons.

  • What is the significance of causal edges in determining black hole properties?

    The number of causal edges going into a black hole can determine its mass, while the curl of these edges can indicate angular momentum. Black holes can have any mass, and mass is assessed by the excess causal edges over normal. Realistic discussions about black holes require a deeper understanding of causal edges and their implications for the properties of these enigmatic cosmic entities.

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Summary

00:00

Exploring Black Holes: Physics Project Updates

  • The goal of the physics project is to explore black holes and the fine structure of black holes.
  • A blog post has been shared detailing the progress and science involved in the project.
  • A general Q&A session about the project is scheduled for Thursday.
  • The summer school, now in its 17th year, will be held as a remote digital experience for the first time, making it more accessible.
  • The primary summer school is three weeks long, focusing on original projects in general Science and Technology, with a new fundamental physics track.
  • A week zero will precede the three-week project time to provide foundational lectures.
  • The project aims to uncover significant findings during the three-week project period.
  • A new Twitter stream, Wolfen physics, will provide detailed updates on live streams and project developments.
  • A forum has been added for open post-publication peer reviews for papers.
  • The project is expanding its Q&A section on the website and enhancing the visual gallery with 3D geometries for potential 3D printing.

18:57

"Black Hole Interior Chaos and Solutions"

  • The remains of a star that formed a black hole generate their own mass, creating a vacuum inside the black hole.
  • Inside a black hole, there is no star, only the origin where Einstein's equations do not apply.
  • The interior solution of a black hole can be chaotic and not well-defined, unlike the exterior solution.
  • Uniqueness theorems apply differently to the exterior and interior solutions of a black hole.
  • The interior solution of a black hole is a vacuum solution, except at the origin where the equations do not apply.
  • Other solutions besides the Schwarzschild solution can exist inside a black hole, with chaotic features.
  • Stephen Hawking proposed a resolution to the black hole information paradox, suggesting apparent horizons instead of true event horizons.
  • The loss of information in black holes may not lead to a loss of unitarity due to chaotic interior solutions.
  • Detecting event horizons in hypergraph systems can be done by plotting graph communities.
  • Superluminal expansion in causal graphs can lead to cosmological event horizons, creating causally disconnected observable universes.

35:09

"Visualizing Universe Connections Through Light Cones"

  • The claim is that a piece of the universe is not fully disconnected from another part, as their future light cones intersect.
  • To visualize this, use vertex out components and highlight the items to understand the connection.
  • Use vertex lists to identify specific points in the graph and determine if their future light cones intersect.
  • To find vertices at a certain level, use the neighborhood graph and specify the layer relative to the root.
  • The goal is to see if future light cones still intersect as the universe evolves.
  • Use the complement of out components to identify vertices at a specific level.
  • Highlight the graph components at a certain level to visualize the connections.
  • Differentiate the induced subgraphs to see how light cones overlap.
  • The aim is to determine if light cones remain connected or if they lead to a black hole.
  • The number of causal edges going into a black hole can determine its mass, while the curl of these edges can indicate angular momentum.

52:39

"Black Holes: Mass, Causal Edges, and Dendrograms"

  • Black holes can have any mass, and mass is assessed by the excess causal edges over normal.
  • Realistic black hole discussion requires more information.
  • No hair theorem is interesting, especially in the context of cosmic event horizons.
  • The shape of the causal graph outside a black hole depends on the total number of causal edges inside.
  • Measurements outside a black hole can be made, possibly related to in-going causal edges.
  • A dendrogram can be created to show how nodes merge at different levels.
  • The distance function for the dendrogram can be determined by the number of levels up.
  • The graph diameter of a causal graph can indicate its width and depth.
  • Flux of causal edges through space-like hyper surfaces is crucial for understanding mass conservation.
  • The depth of a tree can be computed using the adjacency matrix and the number of iterations.

01:11:45

"Graph Distance Matrix for Common Ancestors"

  • The goal is to create a graph distance matrix showing the distance to a common ancestor of each pair of nodes.
  • This can be achieved by calculating the graph distance between pairs of nodes in an undirected graph.
  • To get the graph distance for specific nodes, use different starting and end nodes or specify one vertex to get distances to all others.
  • The aim is to compute the distance matrix for a subset of nodes simultaneously.
  • To select only the lowest-level nodes, pick out the corresponding nodes from the distance matrix.
  • By creating a sub matrix of the lowest-level nodes, a matrix plot can be generated to show distances between them.
  • A histogram of the distances reveals that most nodes are far apart, indicating weak causal connections.
  • The process involves computing the in or out component of the reverse graph iteratively until a common ancestor is found.
  • The function "cousin distance" calculates the number of steps needed to reach a common ancestor for given nodes.
  • The resulting dendrogram displays the relationships and distances between nodes based on their common ancestors.

01:34:52

Analyzing Common Ancestor Distances for Repair

  • Dendogram is being used to analyze common ancestor distances for repair.
  • Standard graph is being examined to understand the situation better.
  • Common ancestor distance is crucial for determining event horizons.
  • Distance function is being utilized to calculate distances between nodes.
  • Asymmetric matrix is generated to show distances between pairs of nodes.
  • Partitioning nodes based on distance criteria is being considered.
  • Histogram is used to visualize common ancestor distances.
  • Longest path is being sought to determine common ancestor distances.
  • Final layer's distance matrix is being computed for analysis.
  • Nodes at specific distances are being identified for further investigation.

01:55:58

Understanding Confluence Merging in Transition Graphs

  • The issue at hand involves understanding the merging of confluence, particularly in relation to events and vertices.
  • A transition matrix is crucial in determining future intersections between sets of vertices.
  • The transition graph depicts which vertices can reach others, with one-way connections indicating black hole-like events.
  • The structure of the transition graph can signify cosmological event horizons or disconnected pieces.
  • Estimating the transition matrix involves analyzing past and future light cone stories to identify causal connections.
  • The goal is to draw the transition matrix based on approximations of null infinity and determine causal connections.
  • The process involves computing adjacency matrices and graphs to assess causal connections at different levels.
  • The analysis aims to distinguish between cosmic and black hole scenarios by testing for directed or undirected graphs.
  • The computation of causal connection graphs for various rules and time steps reveals the evolution of causal connections.
  • The study involves exploring different rules and spatial hypergraphs to understand the connectivity and evolution of causal graphs.

02:15:37

"Exploring Hypergraph Rules and Black Hole Candidates"

  • Initial rules were enumerated and labeled for further analysis.
  • A suggestion was made to compute minimally overlapping initial conditions, but it was deemed not worth the effort.
  • A decision was made to proceed with a specific rule, resulting in 136 cases.
  • The analysis revealed universes with complete graphs that were homogeneous.
  • The presence of fully connected universes at level three was noted.
  • A time constraint was increased to explore more universes.
  • Despite a computing glitch, interesting results were observed, possibly indicating black holes.
  • The idea of using the same code for hypergraphs was proposed.
  • A specific hypergraph rule, 2 goes to 3 2, with 4702 cases was selected for analysis.
  • The process of computing causal connection graphs for different time steps was discussed, revealing potential black hole candidates.

02:38:50

Creating Causal Connection Graphs: Challenges and Insights

  • The process involves creating a graph with specific joins and connections, starting from I and I plus 1, then joining from 20 to 30, and adding an additional join from I to I plus 10.
  • There is confusion about the correct joins, with discussions on visualizing and correcting the graph structure.
  • The goal is to create a causal connection graph, but there are challenges in understanding and implementing the correct connections.
  • The concept of event horizons and causal connections is explored, with a focus on future null infinity and exterior points.
  • The discussion delves into the complexity of detecting event horizons and the need for a clear definition of exterior points.
  • The process involves analyzing future light cones and determining if points are causally connected based on their future interactions.
  • The need for identifying common future light cones and vertex components to establish causal connections is emphasized.
  • The discussion shifts to coding the process, including defining parameters like T for future null infinity and computing the longest path in the graph.
  • The conversation touches on the cosmic censorship hypothesis and its implications for understanding black holes and singularity structures.
  • The dialogue concludes with reflections on the challenges of defining normal forms in general relativity and the concept of future extensibility in PDEs.

02:58:27

Challenges in General Relativity and Fluid Dynamics

  • The Einstein equations can be defined as a time evolution problem on hypersurfaces, leading to maximal future Koshi development.
  • Failures in this development occur in cases of infinite maximal future Koshi development, typically due to singularities.
  • The cosmic censorship conjecture posits that time-like singularities can lead to Cauchy horizons, preventing predictability beyond the singularity.
  • General relativity aims to avoid such singularities, with the strong cosmic censorship conjecture asserting that no extendable future exists from any initial condition.
  • In fluid dynamics, the formation of shocks signifies a violation of strong hyperbolicity, causing characteristic lines to intersect.
  • The failure of global hyperbolicity in general relativity occurs when characteristic lines intersect, indicating a breakdown in the equations' functionality.
  • The fluid case demonstrates that when the velocity field changes faster than the mean free path of molecules, the Navier-Stokes equations cease to apply.
  • The challenge in general relativity lies in understanding the analog of a shock front and deriving additional constraints to address intersections of space-like hypersurfaces.
  • Weak cosmic censorship conjectures suggest that singularities may involve localized violations of causal invariance, impacting the observable universe.
  • The singularity at the center of black holes may lead to violations of causal invariance, potentially associated with quantum issues and particle production.

03:15:28

Evolution of Singularities in Physics Models

  • The singularity theorems suggest that all points evolve independently until they reach a singularity, although the nature of this singularity remains unknown.
  • The discussion delves into the physics of models, exploring the concept of singularity in non-causal invariant systems.
  • Consideration is given to the possibility of a quantum version of fluid systems to investigate shocks and behavior in quantum fluid dynamics.
  • Any initial value problem can be expressed as a multi-way system, allowing for different components to be broken down and computed independently.
  • The conversation shifts to asynchronous cellular automata and Turing machines, highlighting the multi-way evolution in these systems.
  • The concept of event horizons and causal edges within hypergraph theory is explored, discussing the transition from space-like to time-like directions.
  • In the context of rule space, the idea of computational irreducibility and pockets of reusability within event horizons is discussed.
  • The potential analogy between mass and time complexity in rule space is considered, linking it to computational complexity theory.
  • The discussion touches on the computational complexity of rule space and the potential for geometries to inform computational complexity theory.
  • The conversation concludes with ponderings on spacetime singularities, shocks in space-time, and the simulation of black holes through gravitational wave intersections.

03:33:38

"Gravitational Waves and Space-Time Dynamics"

  • Space-time is dynamic and interactions between gravitational waves are significant around black hole formations.
  • Nonlinear waves and interactions are explored, such as gluon field interactions and gravitational wave turbulence.
  • Hadad and Zakharov's recent theorem delves into the interaction between nonlinear gravitational waves and gravitational wave turbulence.
  • A kinetic equation for gravitational wave turbulence is derived with isotropic speck constants.
  • Cosmology models interpret inflation as a byproduct of space-time turbulence.
  • The concept of viscosity in rural space is discussed, with a parabolic damping term in equations.
  • The physics of singularities and the conservation of arithmetic hierarchy are explored.
  • The concept of polynomial convertibility is likened to the growth of geodesic balls in rural space.
  • The analog of the S-matrix for algorithms and the path integral in rural space is considered.
  • The failure of commutativity in covariant derivatives and the uncertainty principle in rural space are discussed in terms of computational complexity theory.

03:48:41

Algorithmic Distance and Physics Project Plans

  • The discussion revolves around polynomial equivalent algorithms, providing a finer notion of distance between algorithms compared to computational complexity hierarchies.
  • Plans are made for future sessions including a QA about the physics project, working on bells inequalities, and continuing the discussion on black holes, with a focus on event horizons.
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