proofofconcept
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20 hours ago •
allofphysicsgraph
allofphysicsgraph
which derivations are relevant for spanning Physics?
Derivations can be categorized by the goal; see https://physicsderivationgraph.blogspot.com/2024/02/derivations-identities-and-other.html
With that context, are any of the proposed derivations https://github.com/allofphysicsgraph/proofofconcept/issues?q=is%3Aopen+is%3Aissue+label%3Aderivation actually connective across domains?
See also
- https://github.com/allofphysicsgraph/proofofconcept/wiki/All-Branches-of-Physics
- https://physicsderivationgraph.blogspot.com/2017/07/finding-edges-for-physics-derivation.html
- https://en.wikipedia.org/wiki/Lists_of_physics_equations
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.
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.
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
}