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HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY 7
and nonpotential effects in hadrons, nuclei and stars that are beyond any dream
of treatment via special relativity.
Therefore, the identification of the limits of applicability of Einsteinian doctrines
and the construction of new relativities are nowadays necessary for scientific
accountability vis-a-vis society, let alone science.
Needless to say, due to the complete symbiosis of special relativity and relativistic
quantum mechanics, the inapplicability of the former implies that of the
latter, and vice-versa. In fact, quantum mechanics will also emerge from our
studies as being only approximately valid for system of particles at short mutual
distances, such as for hadrons, nuclei and stars, for the same technical reasons
implying the lack of exact validity of special relativity.
The resolution of the imbalance due to nonlocal interactions is studied in Chapter
3.
1.2.2 Exterior and Interior Dynamical Problems
The identification of the scientific imbalance here considered requires the knowledge
of the following fundamental distinction:
DEFINITION 1.2.1: Dynamical systems can be classified into:
EXTERIOR DYNAMICAL SYSTEMS, consisting of particles at sufficiently
large mutual distances to permit their point-like approximation under sole actionat-a-distance
interactions, and
INTERIOR DYNAMICAL PROBLEMS, consisting of extended and deformable
particles at mutual distances of the order of their size under action-at-a-distance
interactions as well as contact nonpotential interactions.
Interior and exterior dynamical systems of antiparticles are defined accordingly.
Typical examples of exterior dynamical systems are given by planetary and
atomic structures. Typical examples of interior dynamical systems are given by
the structure of planets at the classical level and by the structure of hadrons,
nuclei, and stars at the operator level.
The distinction of systems into exterior and interior forms dates back to Newton
[2], but was analytically formulated by Lagrange [3], Hamilton [4], Jacobi 3 [5]
and others (see also Whittaker [6] and quoted references). The distinction was
still assumed as fundamental at the beginning of the 20-th century, but thereafter
the distinction was ignored.
3 Contrary to popular belief, the celebrated Jacobi theorem was formulated precisely for the general
analytic equations with external terms, while all reviews known to this author in treatises on mechanics
of the 20-th century present the reduced version of the Jacobi theorem for the equations without external
terms. Consequently, the reading of the original work by Jacobi [5] is strongly recommended over
simplified versions.