The differential equations of Physics
in the theory of Detailed Mechanics
Theories of Physics, including laws expressed by differential equations, can be obtained directly from experimentally measured data by application of the discrete theory of Causal Mechanics (also known as the theory of Detailed Dynamics, or Causal Mathematical Logic) to the data and subsequent use of the mathematical limit. As a simple example, the Euler equations for the rotation of a rigid body are derived directly from a thought experiment performed by an imaginary scientist who lived before Newton or Euler.
The method is completely general and the claim is made that any theory of Physics, discrete or continuous, can be derived by Causal Mathematical Logic directly from experimental measurements, provided all necessary causal information is available and the causal virtual machine is trained with that information.