Notes

Chapter 9: Fundamental Physics


Section 1: The Problems of Physics


Section 2: The Notion of Reversibilityhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-2--the-notion-of-reversibility

Testing for reversibility [in cellular automata] Numbers of reversible [cellular automaton] rules Inverse [cellular automaton] rules Surjectivity and injectivity [in cellular automata] Directional reversibility [in cellular automata] Second-order cellular automata History [of second-order cellular automata] Properties [of second-order cellular automata] Properties [of second-order cellular automata] Generalized additive [cellular automaton] rules Rule 37R Classification of reversible rules Emergence of reversibility Other reversible systems Reversible computation

Section 3: Irreversibility and the Second Law of Thermodynamicshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-3--irreversibility-and-the-second-law-of-thermodynamics

Time reversal invariance History of thermodynamics Current thinking on the Second Law My explanation of the Second Law Biological systems and Maxwell's demon Self-gravitating systems Cosmology and the Second Law Alignment of time in the universe Poincaré recurrence Billiards Entropy of particles in a box Periods in rule 37R

Section 4: Conserved Quantities and Continuum Phenomenahttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-4--conserved-quantities-and-continuum-phenomena

[Conserved quantities in] physics Implementation [of conserved quantity test] More general conserved quantities Other conserved quantities [Conserved quantities in] PDEs Local conservation laws Block cellular automata Block rules [examples] Limiting procedures [for cellular automata] PDE approximations [to cellular automata] Diffusion equation Derivation of the diffusion equation Non-standard diffusion Conservation of vector quantities

Section 5: Ultimate Models for the Universehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-5--ultimate-models-for-the-universe

History of ultimate models [of physics] Theological implications [of ultimate models of physics] [History of] origins of physical models Simplicity in scientific models Numerology Emergence of simple laws Apparent simplicity [of laws] Mechanistic models [in physics] The Anthropic Principle Physics versus mathematics Initial conditions [for the universe] Consequences of an ultimate model [of physics] Meaning of the universe

Section 6: The Nature of Spacehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-6--the-nature-of-space

History of discrete [models of] space Planck length Symmetry [of discrete space] Space and its contents

Section 7: Space as a Networkhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-7--space-as-a-network

Trivalent networks Properties of networks Regular polytopes Generalizations [of trivalent networks] Maintaining simple rules [for networks] 3D network Continuum limits [of networks] Definitions of distance Definitions of dimension Counting of [network] nodes Cycle lengths [in networks] Volumes of spheres Implementation [of network properties] Finding layouts [for networks] Hamming distances [in networks] Continuous mathematics [and networks]

Section 8: The Relationship of Space and Timehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-8--the-relationship-of-space-and-time

History [of views of time] Discreteness in time Network constraint systems Symmetric graphs Cayley graphs Spacetime symmetric rules

Section 9: Time and Causal Networkshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-9--time-and-causal-networks

Causal networks Implementation [of causal networks] [Causal networks for] mobile automata Computational compression [and time] [Causal networks for] 2D mobile automata

Section 10: The Sequencing of Events in the Universehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-10--the-sequencing-of-events-in-the-universe

Implementation [of generalized substitution systems] Generating causal networks The sequential limit [in generalized substitution systems] [Generalized substitution system] rule (b) String theory String overlaps Simulating mobile automata Sequential cellular automata Intrinsic synchronization in cellular automata Distributed computing

Section 11: Uniqueness and Branching in Timehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-11--uniqueness-and-branching-in-time

String transformations Parallel universes Many-worlds models Spacetime networks from multiway systems Commuting operations [on strings] Conditions for convergence [in string rewriting] Confluence [in string rewriting] Completion [in multiway systems] Relationships between types of networks

Section 12: Evolution of Networkshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-12--evolution-of-networks

 Neighbor-independent [network substitution] rules Implementation [of network substitution rules] Identifying subnetworks [in networks] Number of [possible network] replacements Cycles in networks Planar networks [Generating] arbitrary transformations [between networks] [Generating] random networks [Networks generated by] random replacements Cellular structures [in nature] [Network] cluster numbers Non-overlapping [network] clusters 1- and 2-connection [network] clusters Connectedness [of universe] Reversibility [of networks and universe] Feynman diagrams [and networks] Chemical analogy [for network substitutions] Symbolic representations [and networks] Graph grammars Network mobile automata Directed network systems

Section 13: Space, Time and Relativityhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-13--space-time-and-relativity

Posets Spacelike slices Speed of light History of relativity Standard treatment [of relativity] Inferences from relativity Particle physics [and relativity] Time travel

Section 14: Elementary Particleshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-14--elementary-particles

Note for physicists Types of [elementary] particles History [of elementary particles] Topological defects Kuratowski's theorem Gauge invariance Identifying particles [in networks] Knot theory Charge quantization Spin [of particles] Particle masses More particles [in physics] Expansion of the universe

Section 15: The Phenomenon of Gravityhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-15--the-phenomenon-of-gravity

History [of gravity theory] Differential geometry Geodesics Spherical networks Hyperbolic networks Sphere volumes Cylinder volumes [Properties of] discrete spaces Manifold [properties and] undecidability Non-integer dimensions Lorentzian spaces Torsion Random causal networks Einstein equations Pure gravity [theory] Quantum gravity Cosmology

Section 16: Quantum Phenomenahttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-16--quantum-phenomena

History [of quantum theory] Quantum effects Reproducing quantum phenomena Discrete quantum mechanics Feynman diagrams Quantum field theory Vacuum fluctuations  Quantum measurement Bell's inequalities

From Stephen Wolfram: A New Kind of Science [citation]