  The mathematician Leonhard Euler (1707-1783) appears to have been a
philosophical optimist having written: "Since the fabric of universe is the
most perfect and is the work of the most wise Creator, nothing whatsoever take
place in this universe in which some relation of maximum or minimum does not
appear. Wherefore, there is absolutely no doubt that every effect in universe
can be explained as satisfactory from final causes themselves the aid of the
method of Maxima and Minima, as can from the effective causes". Having in mind
this kind of optimism, in the papers [1-16] we introduced and investigated the
possibility to construct a predictive analytic theory of the elementary
particle interaction based on the principle of minimum distance in the space of
quantum states (PMD-SQS). So, choosing the partial transition amplitudes as the
system variational variables and the distance in the space of the quantum
states as a measure of the system effectiveness, we obtained the results
[1-16]. These results proved that the principle of minimum distance in space of
quantum states (PMD-SQS) can be chosen as variational principle by which we can
find the analytic expressions of the partial transition amplitudes. In this
paper we present a description of hadron-hadron scattering via principle of
minimum distance PMD-SQS when the distance in space of states is minimized with
two directional constraints. Then by using the available experimental
(pion-nucleon and kaon-nucleon) phase shifts we obtained not only consistent
experimental tests of the PMD-SQS optimality, but also strong experimental
evidences for new principles in hadronic physics such as: Principle of
nonextensivity conjugation via the Riesz-Thorin relation (1/2p+1/2q=1) and a
new Principle of limited uncertainty in nonextensive quantum physics.
