[AntonioLao]

It can be shown by simple derivations that the repulsive primary force is mass independent. On the other hand it is dependent on the conserved local infinitesimal acceleration of a binary group of space-time points such that the inner product of these quanta of acceleration and the local metric is Lorentz invariant with constant magnitude given by square of light speed.

Starting from Newton’s 2nd law of motion the force F1 due to mass m1 is given by F1=m1a1 where a1 is the inertial acceleration. The force due to m2 is then F2=m2a2. Since the primary forces are equal then F1= F2. This implies that m1a1=m2a2 or m1/m2=a2/a1. Einstein’s mass-energy equivalence implies that E1/E2=m1/m2. Furthermore, if E1 and E2 are respectively the potentials of F1 and F2 then it is also true that E1=r1▪F1 and E2=r2▪F2 therefore (a1▪r1)▪F1=(a2▪r2)▪F2. This is an equation containing triple inner products of vectors. For it to be true one of the inner products is invalid. Since the product of the first would already be a scalar the second inner product would then not be meaningful. The products can be chosen such that a1▪r1= a2▪r2=c and upholding F1= F2.

Since the equation contains only the metric and quantized acceleration, it can be used to establish the validity of Mach’s principle without a definition for mass for the equivalence of quantum mechanical property of spin and the macroscopic property of centrifugal and coriolis forces for all rotating coordinate systems including systems of rigid bodies. It establishes a triple connectivity for Newtonian mechanics, quantum mechanics, and Einstein’s special and general relativity at the local infinitesimal domain of space-time.

The more general implication is that mass is exclusively a property for all secondary attractive forces which are variable forces base on inequalities of their absolute values. However, the absolute values of all primary forces are equal but subjected only to variations in their directional properties. Equality and conservative constancy of absolute values imply repulsions including the general repulsiveness of electric charges and magnetic poles. Since opposite electric charges and opposite magnetic poles attract it can only be implied that at the local infinitesimal domain of space-time their absolute magnitudes cannot truly be equal. In principle this equality and inequality attribute for primary and secondary forces prove indirectly the non-existence of magnetic monopole with one extra condition of time independence (the next topic to be posted).

In closing, a qualitative principle is now possible for all the natural interactions and simply stated as follow: equality repels and inequality attracts.