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Another Face of Force: Inertia Proper

Perhaps the most important consequence of the existence of repulsion as we conceive it here is the fact that, from a quantum mechanical point of view, every particle has a “spin”, an intrinsic kinetic moment. In the past century, this fact appeared as a ravishing discovery, likely to reform the laws of nature. In fact, it is clearly a reflection of the fact that in the “class of acceleration” the Second Law of Newtonian Dynamics is not satisfied. It is very significant that the Wave Mechanics or Quantum Mechanics were actually developed in what we would like to call here the “class of velocity” not in the “class of acceleration”. The principle is as follows: as an empirical fact, the inertia is revealed to human body especially when sudden changes in the velocity occur. The classical acceleration is only an attenuated version of such changes so to speak, obtained from considerations of continuity in time. However, at a sudden change of the velocity, another important physical quantity appears namely the momentum or the quantity of motion. This is a vector quantity, usually denoted by , to which we can attach a differential 1-form, manifested mostly in the process of collision of the material points, which is a process inverse to disintegration:

The attraction still can have here a direct experimental meaning, which can be given in known terms: in a collision the colliding material point tries to impress a velocity to the collided point, while this opposes. This opposition appears as an attraction force towards the colliding material point. Thus, a repulsion can be defined as a differential 2-form given by equation (2) so that the free particle has here the definition

This time the ω is conveniently chosen in the “class of velocities” so that instead of equation (5) we have

where is the velocity vector. This equation defines the material particle in a material point formed of two or more component material points in collision. However, when the case occurs to define one of these component material points, then we define it by the fact that between its material particles there is no repulsion; therefore the left hand side of equation (3′) is zero. Thus, according to (5′) the vectors and must be proportional, and we can write this condition as

This is the classical definition of the momentum given by Newton himself. At the time when the momentum was defined, it was not evident that there is a difference, formally marked by us here, between the coefficient of proportionality from equation (6) and that from equation (8): it has been thought that they represent the same mass. Only later on, when people realized that these coefficients refer to different “classes”, one of them representing the “heavy mass”, the other the “inertial mass”, they proceeded to analyze their identity. The experimental discovery of Eötvös, made with very high precision at the beginning of the last century, that the inertial mass and heavy mass are equal, settled the question and decided the creation of the General Relativity of by Einstein. However, we are especially interested here in the fact that in the space of our experience given by the “velocity class” was always easier to perceive the insufficiency of the Third Principle, as expressed by equation (8) defining the momentum, due to the fact that the Electrodynamics stepped in.

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