which derivations are relevant for spanning Physics? about proofofconcept

[bhpayne]

The https://en.wikipedia.org/wiki/Continuity_equation manifests in multiple domains (different variables, same form and meaning). That isn't what I'm seeking.

[bhpayne]

I may find that there are not connective derivations across domains in Physics. (I don't have a justification why there ought to be connective derivations.)

There are relations like (Maxwell's equations, Schrodinger's equation, the wave equation) that are cross-domain. There's no reason to expect a derivation that involves different assumptions (e.g., the diffusion equation) to relate to Maxwell-Schrodinger-wave.

If that's true, then only the variables and constants and transformations are common across Physics.

I don't get emotional reward from merely writing down expressions and then indexing which expressions have which symbols.

[bhpayne]

https://dreampuf.github.io/GraphvizOnline/

Using subgraphs to denote assumptions doesn't scale well

• (speed of light constant in any frame) xor (speed of light not same in all frames of reference)
• (energy, momentum, angular momentum is continuous) xor (energy, momentum, angular momentum is discrete)

digraph G {
  # https://graphviz.org/docs/attr-types/rankdir/
  #rankdir="LR"; 

  # subgraphs are set of assumptions
  # oval = equation
  # rectangle = topic

  subgraph cluster_assume_mass_and_energy_have_definite_attributes {
    label="ASSUMPTION: matter and energy have definite, knowable attributes such as location in space and speed\nASSUMPTION: matter and energy are continuous (not discrete)";
  
    subgraph cluster_assume_forces_act_instantaneously {
      # Non-relativistic mechanics
      label = "ASSUMPTION: forces act instantaneously";
    
      subgraph cluster_continuous_media {
        label="ASSUMPTION: materials modeled as a continuous medium";
        # SOURCE: https://en.wikipedia.org/wiki/Continuum_mechanics

        # https://en.wikipedia.org/wiki/Continuum_mechanics
        continuum_mechanics [shape=rectangle, label="continuum mechanics"];

        # https://en.wikipedia.org/wiki/Fluid_dynamics
        fluid_dynamics [shape=rectangle, label="fluid dynamics"];

        fluid_dynamics -> continuum_mechanics [label="is subset of"];
        # SOURCE: https://en.wikipedia.org/wiki/Continuum_mechanics
        # which says
        # "The theories of elasticity, plasticity and fluid mechanics are based on the concepts of continuum mechanics."

      }
      subgraph cluster_materials_as_discrete_particles {
        label ="ASSUMPTION: material modeled as ensemble of discrete particles";
        
        # https://en.wikipedia.org/wiki/Statistical_mechanics
        statistical_mechanics [shape=rectangle, label="statistical mechanics"];
        
      }

    
      # https://en.wikipedia.org/wiki/Classical_mechanics
      classical_mechanics [shape=rectangle, label="classical mechanics"];
      
      electromagnetics [shape=rectangle];
      electromagnetics -> classical_mechanics [label="is in domain of"];
      # SOURCE: 

      optics_classical [shape=rectangle, label="classical optics"];
      optics_geometrical_ray [shape=rectangle, label="gemetrical (ray) optics"];
      optics_wave [shape=rectangle, label="wave optics"];
      optics_geometrical_ray -> optics_classical [label="is subset of"];
      # SOURCE: 
      optics_wave -> optics_classical [label="is subset of"];
      # SOURCE: 
  
      optics_classical -> classical_mechanics [label="is subset of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Snell%27s_law
      # aka law of refraction
      snells_law [shape=oval, label="Snell's law"];
      snells_law -> optics_geometrical_ray [label="is in domain of"];
      # SOURCE: 

      snells_law -> brewsters_angle [label="is related to"]; 
      # SOURCE: https://derivationmap.net/review_derivation/522862/?referrer=_table_of_derivations

      brewsters_angle -> optics_geometrical_ray [label="is in domain of"];

      # https://en.wikipedia.org/wiki/Lens#Lensmaker's_equation
      lensmakers_eq [shape=oval, label="Lensmaker's equation"];
      lensmakers_eq -> optics_geometrical_ray [label="is in domain of"];
      # SOURCE: 
  
      interference -> optics_wave [label="is in domain of"];
      # SOURCE: https://en.wikipedia.org/wiki/Optics#Physical_optics
      # which says
      # This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics.
      diffraction -> optics_wave [label="is in domain of"];
      # SOURCE: https://en.wikipedia.org/wiki/Optics#Physical_optics
      # which says
      # This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics.
      

      maxwell_eq [shape=oval, label="Maxwell's equations"];
      maxwell_eq -> electromagnetics [label="is in domain of"];
      # SOURCE: Ben's knowledge

      newtons_law_of_universal_gravitation [label="Newton's law of universal gravitation"];
      newtons_law_of_universal_gravitation -> general_relativity [label="is consistent with"];
      # SOURCE: https://en.wikipedia.org/wiki/General_relativity
      # which says
      # "General relativity generalises special relativity and refines Newton's law of universal gravitation,"
  
      # https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion
      diffusion_eq [shape=oval, label="diffusion equation"];
      diffusion_eq -> classical_mechanics [label="is in domain of"];
      # SOURCE: Ben's knowledge
  
      # https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion
      newtons_laws_of_motion [shape=oval, label="Newton's laws"];
      newtons_laws_of_motion -> classical_mechanics [label="is in domain of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation
      hamilton_jacobi_equation [label="Hamilton-Jacobi equation"];
      hamilton_jacobi_equation -> newtons_laws_of_motion [label="is equivalent to"];
      # SOURCE: 

      # https://en.wikipedia.org/wiki/Gauss%27s_law
      gausss_law [label="Gauss's law"];
      gausss_law -> maxwell_eq [label="is subset of"];
      # SOURCE: 
  
      hookes_law [label="Hooke's law"];
      hookes_law -> classical_mechanics [label="is in domain of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Wave_equation
      wave_eq [label="wave equation"];
      wave_eq -> hookes_law [label="is derived from"];
      # SOURCE: 
  
      wave_eq -> maxwell_eq [label="is related to"];
      # SOURCE: https://derivationmap.net/review_derivation/000004/

      # https://en.wikipedia.org/wiki/Classical_field_theory
      classical_field_theory [shape=rectangle, label="classical field theory"];
  
      fluid_dynamics -> classical_field_theory [label="is subset of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations
      navier_stokes_eq [label="Navier-Stokes equations"];
      navier_stokes_eq -> fluid_dynamics [label="is in domain of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Aerodynamics
      aerodynamics [shape=rectangle];
      aerodynamics -> fluid_dynamics [label="is subset of"];
      # SOURCE: 

      # https://en.wikipedia.org/wiki/Reynolds_number
      reynolds_number [label="Reynolds number"];
      reynolds_number -> fluid_dynamics [label="is in domain of"];
      # SOURCE: 
  
      # https://en.wikipedia.org/wiki/Numerical_weather_prediction
      numerical_weather_prediction [shape=rectangle, label="numerical weather prediction"];
      numerical_weather_prediction -> aerodynamics [label="is in domain of"];
      # SOURCE: 
  
      newtons_law_of_universal_gravitation -> classical_field_theory [label="is in domain of"];
      # SOURCE: 

    }
  }
  


  
  # https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation
  Klein_Gordon_eq [label="Klein-Gordon equation"];
  
  # https://en.wikipedia.org/wiki/Relativistic_wave_equations
  relativistic_wave_eq [shape=rectangle, label="Relativistic wave equations"];
  Klein_Gordon_eq -> relativistic_wave_eq [label="is in domain of"];
  
  relativistic_wave_eq -> quantum_field_theory [label="is in domain of"];
  # SOURCE: https://en.wikipedia.org/wiki/Relativistic_wave_equations
  # which says
  # "In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields."
  
  
  # https://en.wikipedia.org/wiki/Quantum_field_theory
  quantum_field_theory [shape=rectangle, label="quantum field theory"];
  quantum_field_theory -> special_relativity [label="relies on"];
  # SOURCE: https://en.wikipedia.org/wiki/Quantum_field_theory
  # which says
  # "QFT is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics."
  quantum_field_theory -> quantum_mechanics [label="relies on"];
  # SOURCE: https://en.wikipedia.org/wiki/Quantum_field_theory
  # which says
  # "QFT is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics."
  quantum_field_theory -> classical_field_theory [label="relies on"];
  # SOURCE: https://en.wikipedia.org/wiki/Quantum_field_theory
  # which says
  # "QFT is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics."
  
  # https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
  schrodinger_eq [shape=oval, label="Schrodinger's equation"];
  
  # https://en.wikipedia.org/wiki/Quantum_mechanics
  subgraph cluster_discrete_energy_momentum {
    label="ASSUMPTION: discrete values of energy, momentum, angular momentum"
    # SOURCE: https://en.wikipedia.org/wiki/Quantum_mechanics
    
    # I'm less interested in 
    # https://physics.stackexchange.com/questions/463/what-are-the-most-fundamental-assumptions-of-quantum-mechanics
  
    # https://en.wikipedia.org/wiki/Quantum_mechanics
    quantum_mechanics [shape=rectangle, label="quantum mechanics"];
    schrodinger_eq -> quantum_mechanics [label="is in domain of"];
    # SOURCE: Ben's knowledge
  }
  quantum_mechanics -> classical_mechanics [label="is consistent with"];


  subgraph cluster_laws_of_nature_same_in_accelerating_frames {
    label="ASSUMPTION: The laws of nature are the same in different frames of reference (where acceleration is taken into consideration).";
    # SOURCE: https://webhome.auburn.edu/~smith01/notes/relavty.htm
    subgraph cluster_gravitiational_mass_equiv_to_inertial_mass {
      label="ASSUMPTION: Gravitational mass is equivalent to inertial mass.";
      # SOURCE: https://webhome.auburn.edu/~smith01/notes/relavty.htm

      # https://en.wikipedia.org/wiki/General_relativity
      general_relativity [shape=rectangle, label="general relativity"];


    }
  }

  # https://en.wikipedia.org/wiki/Galilean_invariance
  subgraph cluster_galilean_invariance {
    label="ASSUMPTION: laws of physics are invariant (identical) in\n all inertial frames of reference (frames of reference with no acceleration)";
    # SOURCE: https://en.wikipedia.org/wiki/Special_relativity

    subgraph cluster_constant_speed_of_light {
      label="ASSUMPTION: The speed of light in vacuum is the same for all observers, \nregardless of the motion of light source or observer.";
      # SOURCE: https://en.wikipedia.org/wiki/Special_relativity

      # https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
      mass_energy_equivalence [shape=oval, label="E=mc^2"];
      mass_energy_equivalence -> special_relativity [label="is in domain of"];

      # https://en.wikipedia.org/wiki/Special_relativity
      special_relativity [shape=rectangle, label="special relativity"];

      # https://en.wikipedia.org/wiki/Relativistic_Doppler_effect
      relativistic_doppler_effect [shape=oval, label="relativistic Dopper effect"];
      relativistic_doppler_effect -> special_relativity [label="is in domain of"];

    }
  }

  general_relativity -> classical_mechanics [label="is consistent with"];
  # SOURCE: 
  
  special_relativity -> general_relativity [label="is subset of"];
  # SOURCE: 
  
  # https://en.wikipedia.org/wiki/Anderson_localization
  anderson_localization [label="Anderson localization"];
  anderson_localization -> optics_wave [label="is in domain of"];
  # SOURCE: Ben's knowledge
  
  anderson_localization -> quantum_mechanics [label="is in domain of"];
  # SOURCE: https://en.wikipedia.org/wiki/Anderson_localization
  
}