Scaling properties of quantum mechanical equations working as the framework of relativity: Principal articulations about the Lorentz invariant structure of matter

An arbitrary increase of rest masses input to the quantum mechanical description of an atomic or molecular object leads to the increase of the related total energy (i.e., the eigenvalue), and contraction of the size, associated with it. Furthermore, this occurrence, on the basis of the quantum mechanical description in consideration, yields the “invariance” of the quantity [total energy × mass × size²], framing a fundamental architecture, matter is made of. Henceforth, we will call this latter quantity “quantum-mechanical-description-scaling-invariance,” or briefly quantum-mechanical-description-scaling-invariance (QMDSI). This leads, amongst other things, to a whole new systematic of diatomic molecules, in general polyatomic molecules. On the other hand, one can check that the quantity [total energy × mass × size²] happens to be a Lorentz invariant quantity, for one thing; dimensionally, it comes to the square of the action quantity or the square of Planck Constant (which is well Lorentz invariant). Thus, it appears that the QMDSI we disclose about [total energy × mass × size²] with regards to a hypothetical mass change in a quantum mechanical description, happens to work as the inherent mechanism of the end results of the Special Theory of Relativity, was the object in consideration, brought to a uniform translational motion. Or similarly, it comes to work as the innate machinery of the end results of the General Theory of Relativity, where this object is embedded in a gravitational field. In both cases, it is question of a “real, overall mass change,” which in return can well be considered, as an input to the quantum mechanical description, in consideration, to investigate the related results. One can further show that the occurrence we unveil holds not only for a gravitational field but generally for all fields the object at hand interacts with. Note that, herein, we propose to use the word “field,” in the sense of “effective surrounding.” Indeed, in our approach, the related changes take place in the respective cores of the interacting bodies, and not, in a rather fuzzy way, in their environment. Next to the rest masses, there remains one other parameter one can alter in the given quantum mechanical description, of mainly (but without any loss of generality, really), atomistic and molecular objects: It is the product of electric charges, coming into play. Its arbitrary change, in fact, fully reflects the actual Lorentz transformation of electric forces, where the object is brought to a uniform translational motion. Herein, we provide principal mathematical proofs. In a subsequent article, we will disclose the related architecture, matter is made of.