On the Mathematical Modeling of Physical Reality:
"Calculus, in particular, led to accurate mathematical models for physical reality, first in the physical sciences and eventually in the other sciences, engineering, medicine, and business. These mathematical models are usually too complicated to be solved explicitly, and the effort to obtain approximate, but highly useful, solutions gave a major impetus to numerical analysis."
"One of the most important and influential of the early mathematical models in science was that given by Newton to describe the effect of gravity."
from: https://www.britannica.com/science/numerical-analysis/Historical-background
The better the model is, the more accurately it represents physical reality. When complete, the analysis of the model then involves measurement error, phenomena not included (example, 0 or first order models often ignore friction) which leads to comparing the theoretical model to reality, measurements error, precision of references and constants, it's all interrelated.
The best model so far for the atomic world is The Standard Model. From the equations that define the theory, define the model, relationships are defined. These give insight such as relationships that become known as physical laws, like the law of gravitation for a given set of conditions.
So, a wave equation that describes precisely the quantized energy frequency relationship of the electron in an atom of hydrogen contains information about the system. If these terms are carried through to a full analysis, identities can be derived that in the full context of the full model define the interrelationship between all variables.
What if a relationship is found that defines the interrelation of the parameters that define the system? And it has a stable solution to its roots?
A solution that converges no many how many decimals places are targeted?
The statics and dynamics are included.
Maxwell's equations are included.
Boundary conditions are set by all known phenomena.
The equation IS the definition and interrelationship of the parameters that describe the system.
Therefore, the solution to that equation defines the values for that system.
Like the full Rydberg equation (including proton to electron mass ratio and proton radius).
(for a single hydrogen atom)
Thus, the constants and masses of the standard model can be defined mathematically.
As has been shown by this blog and The Oracle (beta 2) code.
The Surfer, OM-IV
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