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Wolfram Physics Project: Working Session Wednesday, May 6, 2020 [Finding Black Hole Structures]

Wolfram・137 minutes read

The discussion delves into various aspects of black holes, including causally disconnected regions, event horizons, and singularity properties, with a focus on optimizing code for analysis. The process involves debugging code to address memory-related issues and explore the behavior of black holes in the context of quantum space and multi-way causal graphs.

Insights

  • The discussion delves into the practical application of determining unreachable events in the context of black holes, emphasizing the importance of non-intersecting future light cones.
  • The concept of singularities is explored, depicting them as space-like instants where everything converges, leading to inevitable collisions, with a distinction made between reasonable physics solutions and those with different initial conditions.
  • The process of merging vertices in a graph using the "vertex contract" method is detailed, involving combining collections of vertices into a single vertex for simplification, with a focus on accurately representing the graph's structure.
  • The analysis of the code's behavior reveals memory-related issues, leading to debugging efforts to resolve memory arrangement discrepancies and potential memory overrides causing crashes, highlighting the importance of code correction and optimization.

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Recent questions

  • What are black holes and their characteristics?

    Black holes are regions in space where gravity is so strong that nothing, not even light, can escape from them. They are formed when massive stars collapse under their gravity, creating a singularity at their center. Black holes have an event horizon, a boundary beyond which nothing can return, and they can vary in size from stellar-mass black holes to supermassive black holes at the centers of galaxies.

  • How do event horizons relate to black holes?

    Event horizons are boundaries around black holes beyond which nothing can escape, not even light. They mark the point of no return for anything falling into a black hole. The event horizon is crucial in defining the properties and behavior of black holes, including their gravitational pull and the formation of singularities at their centers.

  • What is the significance of causally disconnected regions in black holes?

    Causally disconnected regions in black holes refer to areas where events cannot influence each other due to the limitations imposed by the speed of light. This concept is essential in understanding the behavior of black holes, including the formation of event horizons and the trapping of matter within them. Causally disconnected regions play a crucial role in defining the structure and dynamics of black holes in space.

  • How are Penrose diagrams used to understand black holes?

    Penrose diagrams are graphical representations used to visualize the spacetime structure around black holes. They help in understanding the causal relationships, event horizons, and singularities associated with black holes. By studying Penrose diagrams, researchers can gain insights into the complex geometry and physics of black holes, including the evolution of matter and energy within their gravitational fields.

  • What is the Unruh effect in relation to black holes?

    The Unruh effect is a phenomenon similar to Hawking radiation that occurs in accelerating reference frames near black holes. It involves the creation of particles due to the acceleration of an observer, leading to thermal radiation. The Unruh effect provides insights into the quantum effects and dynamics around black holes, shedding light on the interplay between gravity and quantum mechanics in these extreme environments.

Related videos

Summary

00:00

Exploring Black Holes and Causality

  • The discussion focuses on black holes and the continuation of a previous conversation.
  • The speaker plans to delve into the topic of black holes further.
  • A causal graph is mentioned, with new code provided by Jonathan for evaluation.
  • The concept of causally disconnected regions is explained, involving future light cones and unreachable events.
  • The definition of causally disconnected events is discussed, emphasizing non-intersecting future light cones.
  • The distinction between cosmic and black hole event horizons is highlighted.
  • The speaker delves into the practical application of determining unreachable events in the context of black holes.
  • The code provided aims to identify nodes and their unreachable final nodes at specific time steps.
  • An optimization in the code is suggested for clearer understanding and implementation.
  • The speaker contemplates understanding Penrose diagrams for different cases, including extended partial geometry and parallel universes.

22:47

"Exploring Singularities and Event Horizons"

  • The singularity is described as a space-like instant in timing where everything appears, leading to inevitable collision.
  • Singularities are depicted horizontally, trapping all entering objects due to their evolution towards the singularity.
  • Two valid solutions to the Einstein equations are discussed: one with reasonable physics and the other a continuation with different initial conditions.
  • A code has been shared and updated to handle various model cases, including the before model scenario.
  • Penrose diagrams are recommended for understanding cosmological and cosmic singularities, highlighting the physical process and event horizons.
  • The appearance of a black hole creates an event horizon, leading to the collapse of a star towards the singularity.
  • The simulation suggests that creating a time-like singularity is unstable and results in chaotic dynamics.
  • A diagram featuring a cosmic event horizon is examined, showcasing a Kruskal diagram and its limitations in describing cosmic event horizons.
  • The concept of bubble nucleation in a Kasner universe is briefly discussed, along with the complexities of causal connection graphs.
  • The need for a graphical representation to visualize the future connectivity of events at different time steps is explored, considering Venn diagrams and graph plots for set relations.

44:26

"Graph vertices, intersections, and black holes explained"

  • The discussion revolves around the concept of vertices in a graph and their existence at different time steps.
  • The idea of representing intersecting cases with differently indicated edges is proposed.
  • The focus is on understanding the future mixing of evolutions on a space-like hypersurface.
  • The importance of considering causal connectivity on specific space-like hypersurfaces is highlighted.
  • The need to compute intersections and intersection statuses for disconnected regions is emphasized.
  • Different cases are outlined for intersection rules between two lists, including non-intersecting, subset, and equality cases.
  • The significance of identifying causally disconnected regions in a graph is discussed.
  • The concept of event horizons and black holes is introduced in the context of graph theory.
  • The process of finding strongly connected components in a graph to identify black holes is suggested.
  • The proposal to compress each strongly connected component into a single node for clearer representation is made.

01:10:36

Efficient Vertex Merging in Graphs

  • The discussion revolves around merging vertices in a graph to simplify its representation.
  • Initial attempts to merge vertices by connecting all non-first vertices to the first vertex were deemed ineffective.
  • The concept of equivalence classes is introduced to replace every vertex with the first vertex.
  • A method called "vertex contract" is proposed to merge vertices effectively.
  • Vertex contract involves combining collections of vertices into a single vertex in the graph.
  • The process of vertex contract is detailed, including the removal of edges between merged vertices.
  • The discussion delves into the use of fold functions for this process.
  • The creation of a causal connection summary graph is explored, highlighting connected components.
  • The need to label and analyze the levels of vertices in the graph is emphasized.
  • The conversation concludes with a focus on refining the process to accurately represent and analyze the graph's structure.

01:37:14

"Modifying Code for Causal Connection Summary"

  • The goal is to focus on causally connected regions at a specific level.
  • The code needs modification to compute the causal connection graph effectively.
  • There is a discussion on modifying the code to highlight specific vertices at a certain level.
  • The need to compute the causal connection summary is emphasized.
  • There is a debate on the correct interpretation of the generated graphs.
  • The concept of nested black holes within black holes is discussed.
  • Different types of event horizons, including cosmological and black hole event horizons, are identified.
  • An issue with the generation count in the code is highlighted, leading to a failure of global hyperbolicity.
  • The distinction between weakly and strongly connected components is explained.
  • The focus shifts to modifying the code for the Wolfram model case to obtain the causal connection summary function.

02:00:23

"Analyzing causal structures in evolving models"

  • The code uses an evolution function that calls into another function to get a Wolfram model of causally connected regions.
  • The notebook containing the necessary information was sent but may have been in a previous notebook.
  • The causally connected summary needs to be mapped through into another function.
  • The summary depends on the causal connection graph.
  • Different cases and structures are being computed and analyzed.
  • Various cases include black holes in an expanding universe, disjoint cosmological regions, and nested black hole solutions.
  • The process involves computing causal connection summaries and analyzing causal structures.
  • An interactive list selector is used to gather and analyze different cases and rules.
  • Issues with kernel crashes and rogue kernels are causing delays and interruptions in the computation process.
  • Debugging and troubleshooting are ongoing to resolve the issues and continue the analysis.

02:25:53

Troubleshooting parallel kernel crashes and memory leaks

  • Attempted running cases with different configurations and parallel kernels
  • Tried random sampling with four rules and found it to work fine
  • Encountered issues with canonical graph failing on null graph
  • Explored parallel map monitored with map for five cases successfully
  • Faced challenges with SSH connections persistency and potential machine errors
  • Experimented with various parallel evaluation methods and encountered crashes
  • Considered potential issues with AMD Thread Ripper causing crashes
  • Explored different versions of kernels and configurations to troubleshoot crashes
  • Investigated memory leaks and potential data return issues causing crashes
  • Explored hypotheses regarding memory overrides and kernel setups leading to crashes

02:52:16

Debugging code for memory-related issues

  • The issue at hand involves debugging a code that is causing memory-related problems.
  • The focus is on identifying differences in memory arrangement causing the problem.
  • The code is implicated in scribbling on kernel memory, a serious issue that needs resolution.
  • A suggestion is made to try the code without a specific function that has been altered.
  • A mistake in the code is identified, leading to a need for correction.
  • The code is adjusted to ensure the correct function is applied.
  • The debugging process reveals a trivial bug that needs fixing.
  • The code is further modified to ensure the correct function is executed.
  • The analysis of the code's behavior leads to a deeper understanding of its structure and potential issues.
  • The exploration of different initial conditions and parameters sheds light on the code's behavior and potential improvements.

03:15:56

"Black Holes in Multi-Way Causal Graphs"

  • Multi-way golf presents an intriguing concept where black holes may exist on certain branches of the multi-way causal graph but not on others.
  • The interpretation of this phenomenon in quantum space remains a topic of interest, with implications for the fate of black holes in the universe.
  • The development of a connected universe is explored, contrasting cases where connectivity varies across different branches of the multi-way causal graph.
  • The framework for analyzing black holes involves collaborative efforts, primarily led by Max, with contributions from others in optimizing C++ code and developing helper functions.
  • The potential educational value of this framework is highlighted, suggesting its applicability for science fair projects due to its visually appealing nature.
  • Distinctions between cosmic event horizons and black hole graphs are discussed, emphasizing the varying degrees of causal disconnection they represent.
  • The Unruh effect, akin to Hawking radiation in accelerating reference frames, is considered in the context of quantum effects around black holes.
  • The estimation of electron sizes in the causal graph is a complex issue, with suggestions that the underlying hypergraph dynamics occur at a much smaller length scale than conventional particle physics.
  • The exploration of black hole formation in a specific rule reveals complexities in identifying a convincing black hole, prompting further investigation into the multi-way causal graph.
  • The process of computing the multi-way causal graph for black hole formation involves intricate analysis and comparison of causal connections at different levels.

03:34:50

"Level 20 Security and Graph Structures"

  • Discussion about reaching level 20 and using an aspect ratio for security.
  • Mention of a multi-way system and the need for a list.
  • Clarification on arrow precedence and ambiguity in the system.
  • Exploration of causal graphs and states graph structure.
  • Consideration of entanglement horizon and branch-like graphs.
  • Examination of a fractal universe and spatial graph disconnections.
  • Comparison of black hole and cosmological event horizons.
  • Discussion on the no-hair theorem for black holes and detecting properties.
  • Plans to revisit Bell's inequalities in the future.
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