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Chapter 9
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Chapter 9:
Fundamental Physics
Section 1:
The Problems of Physics
There are no notes for this section.
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
"Firing squad" synchronization
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