dichotomy of assumptions

In Physics there are some assumptions that form a dichotomy:

• is the speed of light constant or variable?
• is the measure of energy discrete or continuous?

In the dichotomy of assumptions, one of the two assumptions is reflective of reality, and the other is an oversimplification. The oversimplification is related to reality by assumptions, constraints, and limits. 

(I define "oversimplification" as the extension of useful assumptions to incorrect regions.)

Another case where oversimplification is the link between domains is quantum physics and (classical) statistical physics. Quantum particles are either Fermions (odd half integer spin) or Bosons (integer spin), but that is practically irrelevant for large ensembles of particles at room temperature. The aspects that get measured at one scale (e.g., particle velocity) are related to but separate from metrics at another scale (e.g, temperature, entropy). Mathematically this transition manifests as the switch from summation to integration.

So what? 
This is a new-to-me category of derivations which span domains. What constitutes a domain is set by the assumptions that form the boundaries, and oversimplification is how to cross the boundaries. 

What boundaries should the Physics Derivation Graph transgress? What oversimplifications are adjacent?

• quantum mechanics to classical - https://en.wikipedia.org/wiki/Canonical_quantization
• https://en.wikipedia.org/wiki/Optics
• https://en.wikipedia.org/wiki/Condensed_matter_physics
• https://en.wikipedia.org/wiki/Statistical_mechanics
• https://scholar.harvard.edu/files/schwartz/files/10-quantumstatmech_0.pdf
• https://physics.stackexchange.com/questions/374647/for-ideal-classical-gasses-in-terms-of-the-energy-levels-why-do-we-ignore-wheth
• relativity to classical
• https://en.wikipedia.org/wiki/Astrometry
• https://en.wikipedia.org/wiki/Orbital_mechanics
• https://en.wikipedia.org/wiki/Celestial_mechanics
• https://en.wikipedia.org/wiki/Galactic_astronomy
• https://en.wikipedia.org/wiki/Astronomy#Stellar_astronomy
• https://physics.stackexchange.com/questions/580494/difference-between-relativistic-and-non-relativistic-classical-equations-of-elec
• "The EFE reduce to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation." source
• quantum field theory to quantum mechanics
• https://en.wikipedia.org/wiki/Quantum_field_theory#Mathematical_rigor -- see particle in a box

The evidences of dissonance (e.g, Mercury’s perihelion based on Newtonian gravitation versus relativity, the Deflection of Starlight; source) are not relevant for bridging domains. They are illustrations of the oversimplification.

Update 2024-03-10: on the page https://en.wikipedia.org/wiki/Phase_space#Quantum_mechanics

"by expressing quantum mechanics in phase space (the same ambit as for classical mechanics), the Weyl map facilitates recognition of quantum mechanics as a deformation (generalization) of classical mechanics, with deformation parameter ħ/S, where S is the action of the relevant process. (Other familiar deformations in physics involve the deformation of classical Newtonian into relativistic mechanics, with deformation parameter v/c; or the deformation of Newtonian gravity into general relativity, with deformation parameter Schwarzschild radius/characteristic dimension.)
 
Classical expressions, observables, and operations (such as Poisson brackets) are modified by ħ-dependent quantum corrections, as the conventional commutative multiplication applying in classical mechanics is generalized to the noncommutative star-multiplication characterizing quantum mechanics and underlying its uncertainty principle."

See also https://en.wikipedia.org/wiki/Wigner%E2%80%93Weyl_transform#Deformation_quantization