Monday, July 3, 2017

finding major edges of the Physics Derivation Graph

I've decided to focus on building content for the Physics Derivation Graph. Since I don't think it's reasonable to enter all the mathematical physics content manually on my own, in this post I'll define some bounds.

Step 1: identify major fields in Physics
  • Electromagnetism
  • relativity
    • astrophysics
  • quantum mechanics
  • classical mechanics
    • thermodynamics
Step 2: identify top derivations associated with each area
  • Electromagnetism: Maxwell's equations
  • Relativity: Lorentz (time dilation, length contraction)
    • astrophysics: 
  • Quantum mechanics: Schrodinger, Uncertainty
  • Classical mechanics: F=ma, conservation of energy and momentum
    • thermodynamics: entropy

Step 3: 

There are expressions, domains, and notations that need to be included to demonstrate the comprehensive nature of the project and the capability of the framework.

Schrodinger's equationQuantumDirac/bra-ket

Maxwell's equationsElectromagneticsdifferentiation, vectors
contravariant/covariantElectrodynamicsEinstein notation
Navier StokesFluid Mechanicsdifferentiation, vectors
mass-energy relation
Special Relativity
Uncertainty relationQuantum Mechanics
energy conservationclassical mechanics
string theory
wave equation
statistical mechanics
simple harmonic oscillator

Other comprehensive lists of "things to know" in Physics

The Physics Derivation Graph has a few pertinent scales:
In this post, I'll focus on finding examples of derivations linking the major expressions

Useful places to search

  • Google Scholar
  • Arxiv
  • journals for Physics teachers
Useful search string: derivation of equation

Unsorted results–Lorentz_force's_equation_of_motion–Lambert_law's_theorem–Salpeter_equation–Scholes_model–Einstein_statistics–gram–second_system_of_units–Clapeyron_relation's_law–Bernoulli_beam_theory–Maclaurin_formula's_principle's_laws_of_diffusion–Huggins_solution_theory–Rubin_compactification–Nuttall_law–Duhem_equation–Painlevé_coordinates–Jacobi_equation–Shockley_experiment–Gordon_equation–Kronig_relations–Wannier_duality–Joukowski_theoreménard–Wiechert_potential–Schwinger_equation–energy_equivalence–Boltzmann_statistics–Rivlin_solid's_theorem_of_revolving_orbits's_theorem's_law's_law–Boltzmann_equation's_theorem'_rotation_formulaödinger_equation–Dyson_equation–Boltzmann_law's_theorem
tag: math
tag: weather
tag: math

Seismic Wave Equation
tag: PDF

Noether's theorem

E=mc2 and F=ma
Ives, Herbert E. (1952), "Derivation of the mass–energy relation", Journal of the Optical Society of America, 42 (8): 540–543, doi:10.1364/JOSA.42.000540   | tag: paywall
On the page
there's a step which involves
--> I don't understand the third line of equations. The infinitesimal switches from ds to d(mv), and the integration limit changes.
Derivation of Electromagnetic Waves from Maxwell’s Equations
tag: PDF
Maxwell's equations as presented in Feynman's lectures
Feynman's derivation of Maxwell equations and extra dimensions:

derivation of the time‐dependent convective‐diffusion equation for surfactant transport along a deforming interface
tag: paywall

Derivation of the Continuous-Time Random-Walk Equation
tag: paywall

derivation of the chemical master equation
tag: paywall

Derivation of Kramer's equation, friction coefficient, and macroscopic laws for physisorption
tag: paywall

tag: PDF

derivation of an equation for predicting minimum spouting velocity - DOI: 10.1002/aic.690040423
tag: paywall

Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current
tag: paywall

Classical mechanics

Derivation of Kepler's laws
Heat and Diffusion Equation in Space and Time
tag: PDF
Derivation of the Diffusion Equation
tag: PDF

Derivation of Diffusion Equation
tag: PDF

Relation between F=ma and Newton's Second Law of Motion

Rocket equation

A New Derivation of Jeffery’s Equation -- DOI: 10.1007/s00021-005-0208-0
tag: paywall, PDF



kirchoff current law and kirchoff voltage law
tag: PDF

Thermal, aka statistical, mechanics

Local thermodynamic derivation of Young's equation
tag: paywall, PDF

Derivation of the Boltzmann principle
tag: PDF

Boltzmann distribution

Note on the derivation of the Boltzmann equation from the Liouville equation
tag: paywall, PDF

tag: PDF

Derivation of the Ideal Gas Law
DOI: 10.1021/ed084p1832
tag: PDF

Quantum Mechanics
Deriving time dependent Schrödinger equation from Wave-Mechanics
tag: PDF
Derivation of Schrödinger's equation from stochastic electrodynamics -DOI: 10.1007/BF00670387
tag: paywall
Covariant Feynman derivation of Schrodinger's equation in a riemannian space
tag: paywall, PDF

Derivation of the Dirac equation from a relativistic representation of spin
tag: paywall, PDF
Physical meaning and derivation of Schrodinger and Dirac equations
tag: arxiv

The Dirac Equation
tag: PDF

Particle in a 1D box


Thermodynamic derivation of Saha's equation for a multi-temperature plasma
tag: paywall, PDF

The Einstein and the Navier-Stokes Equations: Connecting the Two by Bredberg, Irene, Ph.D., HARVARD UNIVERSITY, 2012, 132 pages; 3513905
Abstract: This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics.
see also

Relation between uncertainty and the quantum harmonic oscillator

Schrodinger equation and quantum harmonic oscillator

Schrodinger equation and wave equation

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