Chapter 9: Fundamental Physics

Section 1: The Problems of Physics

Section 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 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 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 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 Space

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

Section 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 Time

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

Section 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 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 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 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 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 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 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 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]