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Relation Between Action at Distance and Force

What is the situation regarding attraction and repulsion in Science right now? We can summarize it simply by saying that the repulsion is thought in terms of attraction; that between the two there is no conceptual difference: they are simply characteristics of the force, as this concept descended to us from Newton. In order to demonstrate the point, we offer a graphical illustration in the figure below.

The full curve from this figure represents the attraction force inversely proportional with the square of the distance r between particles. If this force is universal, as Newton inferred, then it acts even between the particles constituting a physical body. Therefore, no body could really exist, but would collapse under the very force of attraction of its components. This is, obviously, not what we really observe. Thus the law of universal attraction has been duly amended, in order to correspond to the facts. An example is that of Seeliger paradox considered by Einstein (Einstein, 1920), and presented here in excerpt in a previous section. This amendment goes, however, no further than the idea of force. First, the force acts by attraction from infinity up to a distance marked r₁ on our figure; then the force changes and acts by repulsion from r₁ to an even smaller distance r₀ between the particles where it starts again acting by attraction. This amendment has also been noticed as worthy of consideration by Newton himself. Later on, in the 19^th century, when the geometrical and analytical tools have matured enough, the idea took interesting turns in explaining the cohesion of solids, the theory of stresses, the theory of ideal and real gases, etc. The analytical considerations of this sort gave it that power of persuasion characteristic to every theory that can be deduced from a minimum of hypotheses by simple logical arguments, which are obviously natural in the free creations of the intellect.

     One thing, however, Science failed to notice, namely that in this process the attraction and repulsion were made attributes of the concepts of force, their difference being not qualitative as conferred to them by observation, but quantitative as conferred by the space extension. This fact led to many important scientific conquests, but also to much confusion, insofar as the Natural Philosophy has been deprived of a host of mathematical possibilities which came only later to be available. However, when they came into existence the damage was already there in the form of the impassable gap between Science and Bible as we witness it today. In short then, the logic of these concepts was arraigned by pure philosophers. Kant for instance, to name one of the most representatives of the human spirits, noticed that the attraction and repulsion are the concepts granted to us in order to be able to follow the God’s path in building the World. Then Hegel noticed that actually the relation between attraction, repulsion and force is kind of inverse to that thought of by the natural philosophers: in fact it is the force that enters as an attribute of attraction and repulsion, not vice versa. Indeed, we can think of the force without either attraction or repulsion (this is the way it has come into being!) but attraction and repulsion cannot be considered without force. Any such consideration is pure imagination! The attraction and repulsion, continues Hegel, are opposite to one another, and according to his Dialectic they cannot exist separately (Hegel, 1991).

     This fact can be easily explained speculatively, as a natural philosophical fact, with the two concepts of material particle and material point introduced by Hertz. Indeed there is no attraction without repulsion, because only by repulsion the particles are maintaining their identity in a material point. On the other hand, there is no repulsion without attraction, for only by attraction the material points can exist, if it is true that a material point is composed of material particles. This is actually the fundamental idea to start with, and it was indeed this logic the one which selected the path of development of the Science, helping it become what we see today. It is then obvious that the force must have here the rank that all the concepts of Analytical Geometry for instance have, i.e. it must help in logical explanation of the relationship between repulsion and attraction. To underline it once more, it is the force which is a determination of either attraction or repulsion, and not vice versa.

     This observation has the nice merit to direct in a precise way our effort of understanding the concepts of attraction and repulsion as we actually notice and infer them from our experience: we notice them as forces and infer that they are actions at distance. That in this process we are thinking that the attraction and repulsion are actually realized by force comes only as secondary. As a matter of fact it is worth noticing that the force has to be pushed even further back among our priorities here, when recalling that the attraction and repulsion are actually actions at distance which, only when accomplished through matter are forces. Then, again, are there any other kinds of action at distance? We can count on one of them precisely: the light! It is the only action at distance revealed to us by senses, even though it doesn’t appeal to the same senses as the force. There might be some other kinds of action at distance, but momentarily we don’t seem to have senses for them. Well, at least not all of us!

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