Notes
Chapter 9: Fundamental Physics
Section 2: The Notion of Reversibility
https://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-2--the-notion-of-reversibility
![Testing for reversibility [in cellular automata]](/nks/img/thumbnails/notes-9-2--testing-for-reversibility-in-cellular-automata--textonly.png "Testing for reversibility [in cellular automata]")
![Numbers of reversible [cellular automaton] rules](/nks/img/thumbnails/notes-9-2--numbers-of-reversible-cellular-automaton-rules--textonly.png "Numbers of reversible [cellular automaton] rules")
![Inverse [cellular automaton] rules](/nks/img/thumbnails/notes-9-2--inverse-cellular-automaton-rules--textonly.png "Inverse [cellular automaton] rules")
![Surjectivity and injectivity [in cellular automata]](/nks/img/thumbnails/notes-9-2--surjectivity-and-injectivity-in-cellular-automata--textonly.png "Surjectivity and injectivity [in cellular automata]")
![Directional reversibility [in cellular automata]](/nks/img/thumbnails/notes-9-2--directional-reversibility-in-cellular-automata--textonly.png "Directional reversibility [in cellular automata]")
![History [of second-order cellular automata]](/nks/img/thumbnails/notes-9-2--history-of-second-order-cellular-automata--textonly.png "History [of second-order cellular automata]")
![Properties [of second-order cellular automata]](/nks/img/thumbnails/notes-9-2--properties-of-second-order-cellular-automata-1--textonly.png "Properties [of second-order cellular automata]")
![Properties [of second-order cellular automata]](/nks/img/thumbnails/notes-9-2--properties-of-second-order-cellular-automata-2--textonly.png "Properties [of second-order cellular automata]")
![Generalized additive [cellular automaton] rules](/nks/img/thumbnails/notes-9-2--generalized-additive-cellular-automaton-rules--textonly.png "Generalized additive [cellular automaton] rules")
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
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
Current thinking on the Second Law
My explanation of the Second Law
Biological systems and Maxwell's demon
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](/nks/img/thumbnails/notes-9-4--conserved-quantities-in-physics--textonly.png "[Conserved quantities in] physics")
![Implementation [of conserved quantity test]](/nks/img/thumbnails/notes-9-4--implementation-of-conserved-quantity-test--textonly.png "Implementation [of conserved quantity test]")
![[Conserved quantities in] PDEs](/nks/img/thumbnails/notes-9-4--conserved-quantities-in-pdes--textonly.png "[Conserved quantities in] PDEs")
![Block rules [examples]](/nks/img/thumbnails/notes-9-4--block-rules-examples--textonly.png "Block rules [examples]")
![Limiting procedures [for cellular automata]](/nks/img/thumbnails/notes-9-4--limiting-procedures-for-cellular-automata--textonly.png "Limiting procedures [for cellular automata]")
![PDE approximations [to cellular automata]](/nks/img/thumbnails/notes-9-4--pde-approximations-to-cellular-automata--textonly.png "PDE approximations [to cellular automata]")
[Conserved quantities in] physics
Implementation [of conserved quantity test]
More general conserved quantities
[Conserved quantities in] PDEs
Limiting procedures [for cellular automata]
PDE approximations [to cellular automata]
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]](/nks/img/thumbnails/notes-9-5--history-of-ultimate-models-of-physics--textonly.png "History of ultimate models [of physics]")
![Theological implications [of ultimate models of physics]](/nks/img/thumbnails/notes-9-5--theological-implications-of-ultimate-models-of-physics--textonly.png "Theological implications [of ultimate models of physics]")
![[History of] origins of physical models](/nks/img/thumbnails/notes-9-5--history-of-origins-of-physical-models--textonly.png "[History of] origins of physical models")
![Apparent simplicity [of laws]](/nks/img/thumbnails/notes-9-5--apparent-simplicity-of-laws--textonly.png "Apparent simplicity [of laws]")
![Mechanistic models [in physics]](/nks/img/thumbnails/notes-9-5--mechanistic-models-in-physics--textonly.png "Mechanistic models [in physics]")
![Initial conditions [for the universe]](/nks/img/thumbnails/notes-9-5--initial-conditions-for-the-universe--textonly.png "Initial conditions [for the universe]")
![Consequences of an ultimate model [of physics]](/nks/img/thumbnails/notes-9-5--consequences-of-an-ultimate-model-of-physics--textonly.png "Consequences of an ultimate model [of physics]")
History of ultimate models [of physics]
Theological implications [of ultimate models of physics]
[History of] origins of physical models
Simplicity in scientific models
Mechanistic models [in physics]
Initial conditions [for 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](/nks/img/thumbnails/notes-9-6--history-of-discrete-models-of-space--textonly.png "History of discrete [models of] space")
![Symmetry [of discrete space]](/nks/img/thumbnails/notes-9-6--symmetry-of-discrete-space--textonly.png "Symmetry [of discrete space]")
Section 7: Space as a Networkhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-7--space-as-a-network
![Generalizations [of trivalent networks]](/nks/img/thumbnails/notes-9-7--generalizations-of-trivalent-networks--textonly.png "Generalizations [of trivalent networks]")
![Maintaining simple rules [for networks]](/nks/img/thumbnails/notes-9-7--maintaining-simple-rules-for-networks--textonly.png "Maintaining simple rules [for networks]")
![Continuum limits [of networks]](/nks/img/thumbnails/notes-9-7--continuum-limits-of-networks--textonly.png "Continuum limits [of networks]")
![Counting of [network] nodes](/nks/img/thumbnails/notes-9-7--counting-of-network-nodes--textonly.png "Counting of [network] nodes")
![Cycle lengths [in networks]](/nks/img/thumbnails/notes-9-7--cycle-lengths-in-networks--textonly.png "Cycle lengths [in networks]")
![Implementation [of network properties]](/nks/img/thumbnails/notes-9-7--implementation-of-network-properties--textonly.png "Implementation [of network properties]")
![Finding layouts [for networks]](/nks/img/thumbnails/notes-9-7--finding-layouts-for-networks--textonly.png "Finding layouts [for networks]")
![Hamming distances [in networks]](/nks/img/thumbnails/notes-9-7--hamming-distances-in-networks--textonly.png "Hamming distances [in networks]")
![Continuous mathematics [and networks]](/nks/img/thumbnails/notes-9-7--continuous-mathematics-and-networks--textonly.png "Continuous mathematics [and networks]")
Generalizations [of trivalent networks]
Maintaining simple rules [for networks]
Continuum limits [of networks]
Implementation [of network properties]
Finding layouts [for 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]](/nks/img/thumbnails/notes-9-8--history-of-views-of-time--textonly.png "History [of views of time]")
Section 9: Time and Causal Networkshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-9--time-and-causal-networks
![Implementation [of causal networks]](/nks/img/thumbnails/notes-9-9--implementation-of-causal-networks--textonly.png "Implementation [of causal networks]")
![[Causal networks for] mobile automata](/nks/img/thumbnails/notes-9-9--causal-networks-for-mobile-automata--textonly.png "[Causal networks for] mobile automata")
![Computational compression [and time]](/nks/img/thumbnails/notes-9-9--computational-compression-and-time--textonly.png "Computational compression [and time]")
![[Causal networks for] 2D mobile automata](/nks/img/thumbnails/notes-9-9--causal-networks-for-2d-mobile-automata--textonly.png "[Causal networks for] 2D mobile automata")
Implementation [of causal networks]
[Causal networks for] 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]](/nks/img/thumbnails/notes-9-10--implementation-of-generalized-substitution-systems--textonly.png "Implementation [of generalized substitution systems]")
![The sequential limit [in generalized substitution systems]](/nks/img/thumbnails/notes-9-10--the-sequential-limit-in-generalized-substitution-systems--textonly.png "The sequential limit [in generalized substitution systems]")
![[Generalized substitution system] rule (b)](/nks/img/thumbnails/notes-9-10--generalized-substitution-system-rule-b--textonly.png "[Generalized substitution system] rule (b)")
Implementation [of generalized substitution systems]
The sequential limit [in generalized substitution systems]
[Generalized substitution system] rule (b)
Intrinsic synchronization in cellular automata
Section 11: Uniqueness and Branching in Timehttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-11--uniqueness-and-branching-in-time
![Commuting operations [on strings]](/nks/img/thumbnails/notes-9-11--commuting-operations-on-strings--textonly.png "Commuting operations [on strings]")
![Conditions for convergence [in string rewriting]](/nks/img/thumbnails/notes-9-11--conditions-for-convergence-in-string-rewriting--textonly.png "Conditions for convergence [in string rewriting]")
![Confluence [in string rewriting]](/nks/img/thumbnails/notes-9-11--confluence-in-string-rewriting--textonly.png "Confluence [in string rewriting]")
![Completion [in multiway systems]](/nks/img/thumbnails/notes-9-11--completion-in-multiway-systems--textonly.png "Completion [in multiway systems]")
Spacetime networks from multiway systems
Commuting operations [on strings]
Conditions for convergence [in string rewriting]
Confluence [in string rewriting]
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](/nks/img/thumbnails/notes-9-12--neighbor-independent-network-substitution-rules--textonly.png "Neighbor-independent [network substitution] rules")
![Implementation [of network substitution rules]](/nks/img/thumbnails/notes-9-12--implementation-of-network-substitution-rules--textonly.png "Implementation [of network substitution rules]")
![Identifying subnetworks [in networks]](/nks/img/thumbnails/notes-9-12--identifying-subnetworks-in-networks--textonly.png "Identifying subnetworks [in networks]")
![Number of [possible network] replacements](/nks/img/thumbnails/notes-9-12--number-of-possible-network-replacements--textonly.png "Number of [possible network] replacements")
![[Generating] arbitrary transformations [between networks]](/nks/img/thumbnails/notes-9-12--generating-arbitrary-transformations-between-networks--textonly.png "[Generating] arbitrary transformations [between networks]")
![[Generating] random networks](/nks/img/thumbnails/notes-9-12--generating-random-networks--textonly.png "[Generating] random networks")
![[Networks generated by] random replacements](/nks/img/thumbnails/notes-9-12--networks-generated-by-random-replacements--textonly.png "[Networks generated by] random replacements")
![Cellular structures [in nature]](/nks/img/thumbnails/notes-9-12--cellular-structures-in-nature--textonly.png "Cellular structures [in nature]")
![[Network] cluster numbers](/nks/img/thumbnails/notes-9-12--network-cluster-numbers--textonly.png "[Network] cluster numbers")
![Non-overlapping [network] clusters](/nks/img/thumbnails/notes-9-12--non-overlapping-network-clusters--textonly.png "Non-overlapping [network] clusters")
![1- and 2-connection [network] clusters](/nks/img/thumbnails/notes-9-12--1-and-2-connection-network-clusters--textonly.png "1- and 2-connection [network] clusters")
![Connectedness [of universe]](/nks/img/thumbnails/notes-9-12--connectedness-of-universe--textonly.png "Connectedness [of universe]")
![Reversibility [of networks and universe]](/nks/img/thumbnails/notes-9-12--reversibility-of-networks-and-universe--textonly.png "Reversibility [of networks and universe]")
![Feynman diagrams [and networks]](/nks/img/thumbnails/notes-9-12--feynman-diagrams-and-networks--textonly.png "Feynman diagrams [and networks]")
![Chemical analogy [for network substitutions]](/nks/img/thumbnails/notes-9-12--chemical-analogy-for-network-substitutions--textonly.png "Chemical analogy [for network substitutions]")
![Symbolic representations [and networks]](/nks/img/thumbnails/notes-9-12--symbolic-representations-and-networks--textonly.png "Symbolic representations [and networks]")
Neighbor-independent [network substitution] rules
Implementation [of network substitution rules]
Identifying subnetworks [in networks]
Number of [possible network] replacements
[Generating] arbitrary transformations [between networks]
[Networks generated by] random replacements
Cellular structures [in nature]
Non-overlapping [network] clusters
1- and 2-connection [network] clusters
Reversibility [of networks and universe]
Feynman diagrams [and networks]
Chemical analogy [for network substitutions]
Section 13: Space, Time and Relativityhttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-13--space-time-and-relativity
![Standard treatment [of relativity]](/nks/img/thumbnails/notes-9-13--standard-treatment-of-relativity--textonly.png "Standard treatment [of relativity]")
![Particle physics [and relativity]](/nks/img/thumbnails/notes-9-13--particle-physics-and-relativity--textonly.png "Particle physics [and relativity]")
Section 14: Elementary Particleshttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-14--elementary-particles
![Types of [elementary] particles](/nks/img/thumbnails/notes-9-14--types-of-elementary-particles--textonly.png "Types of [elementary] particles")
![History [of elementary particles]](/nks/img/thumbnails/notes-9-14--history-of-elementary-particles--textonly.png "History [of elementary particles]")
![Identifying particles [in networks]](/nks/img/thumbnails/notes-9-14--identifying-particles-in-networks--textonly.png "Identifying particles [in networks]")
![Spin [of particles]](/nks/img/thumbnails/notes-9-14--spin-of-particles--textonly.png "Spin [of particles]")
![More particles [in physics]](/nks/img/thumbnails/notes-9-14--more-particles-in-physics--textonly.png "More particles [in physics]")
Types of [elementary] particles
History [of elementary particles]
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]](/nks/img/thumbnails/notes-9-15--history-of-gravity-theory--textonly.png "History [of gravity theory]")
![[Properties of] discrete spaces](/nks/img/thumbnails/notes-9-15--properties-of-discrete-spaces--textonly.png "[Properties of] discrete spaces")
![Manifold [properties and] undecidability](/nks/img/thumbnails/notes-9-15--manifold-properties-and-undecidability--textonly.png "Manifold [properties and] undecidability")
![Pure gravity [theory]](/nks/img/thumbnails/notes-9-15--pure-gravity-theory--textonly.png "Pure gravity [theory]")
Section 16: Quantum Phenomenahttps://www.wolframscience.com/nks/chap-9--fundamental-physics--notes#sect-9-16--quantum-phenomena
![History [of quantum theory]](/nks/img/thumbnails/notes-9-16--history-of-quantum-theory--textonly.png "History [of quantum theory]")
