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Quantum Mechanics and the Theory of Ensembles

In order to picture the liberalism of the Hertzian perception a little closer, let’s remind once again that, within the Newtonian System, the material point and material particle are always identified with each other. Both have the characteristics of what Hertz calls material particle, i.e. they are both invariable and indestructible. This has been recognized in the last century as one of the basic weaknesses of the Classical Mechanics, which has been corrected by the Quantum Mechanics, when this was applied to the description of the collision processes. It is this way that the Quantum Theory of Fields has made its appearance, with a special description of the creation and annihilation of the particles, processes mostly related to the name of Dirac. This whole history meant a direct recognition of the fact that there are determinations of the concept of classical particle for which indestructibility did not work. In fact, the basis of this situation, which is provided by the Quantum Mechanics, is contained in the Hertz’s Definition 1 quoted above. What Quantum Mechanics did there was to eliminate from that definition the words “without ambiguity” for the association between the points in space, and therefore for the association between the points in space and the moments of time. And historically it is the contradiction between the idea of localization of a material point (implied by its classical acceptance as material particle) and the space extension of this material point, which led to the Wave Mechanics in its first formulation.

     The ensemble of particles entering the structure of a material point is not a simple physical structure to think about. First of all, in Hertz’s way of thinking it demands an infinite number of particles, and this infinite takes here the transcendent determination given to it, just about the time when Hertz wrote his Mechanics, by Dedekind, Cantor and a little later by Zermelo. Secondly, in order to see what the concept of material point entails from a dynamical point of view, one has to keep in mind that the particles have to maintain their identity, no matter if free or components of a material point. This is again, implied by the same invariability and indestructibility properties of a material particle. Indeed, when it comes to the reality of the concept of material point, one can readily see that the constitution of such a point needs repulsion forces between its particles, in order for these to preserve their identity. Therefore inside a material point any particle possesses repulsion towards all the other particles of the material point. On the other hand, unlike the material particle, a material point must be variable and destructible. This also requires that between its material particles there is cohesion, for otherwise the material point could not exist; therefore a material particle in a material point possesses attraction towards all the other particles of the material point. It is most unfortunate that this fact is usually taken merely as a formal mind process of a speculative nature. Not that to a certain extent it is not such a process, but a pure speculation without the belief that it corresponds to a physical construction can lead anywhere, as it indeed already did.

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