Empirical relationship as a stepping-stone to theory

We consider parsimonious construction of empirical equations, to promote interest in them as a stepping-stone model to the physical law. To this end, we provide a variety of historical examples and simulate a parsimonious empirical calculation of Planck law, and of van der Waals equation. Thereby we provide a) Empirical forms of Planck law, and b) Collation of verified symmetries and catastrophes-like properties of empirical P-T surface of real gases. An empirical equation of state for a real gas should take account of these properties.

Modeling of the long-time asymptotic dynamics of a point-like object

We introduce four original concepts: First, the point-like object (PO) specified as a classical extended real object whose response to an external force is aptly specified solely by the trajectory of a single point, whose velocity eventually stops changing after the cessation of the external force. Second, the dynamic models of an PO that generalize the Newton second law by the explicit modeling of PO-acceleration by nonlinear functions of the external force. Third, the long-time asymptotic dynamics of an PO (LTAD) modeled by polynomials in time-derivatives of the external force (by LTAD-models). To make LTAD-models we do not need to know the PO equation of motion. Given the PO equation of motion, without solving it, we can calculate the appropriate LTAD-models, but not vice verse. Fourth, the asymptotic differential equations about the LTAD. They are equivalent to the LTAD-models, but not to the PO equation of motion. To resolve the conceptual controversy surrounding the relativistic Lorentz-Abraham-Dirac equation, we interpret this equation as an asymptotic differential equation about the LTAD of an electrified PO, and not as a differential equation of motion for an electrified PO. Keywords: Point-like; asymptotic dynamics; cyclic motion; differential equation; Lorentz-Abraham-Dirac equation

Modeling quantum scattering of fundamental particles by classical, deterministic processes

We point out that results obtained by M. Ribaric and L. Sustersic, hep-th/0403084, and by M. Blasone, P. Jizba and H. Kleinert, quant-ph/0409021, suggest that the path-integral formalism is the key to a derivation of quantum physics from classical, deterministic physics in the four-dimensional space-time. These results and the t Hooft conjecture, hep-th/0104219, suggest to consider a relativistic, non-material medium, an ether, as a base for non-local hidden-variable models of the physical universe.