A New Mathematical Definition of the Concept of Force
Keywords: concept of force, field, scalar potential, field constant, field potential, field strength
The concept of force may be mathematically expressed in such a way that a force may be defined for every quantity that a field con-serves. The components (in italics) of this definition are defined individually in statements that may be translated into mathematical language: 1) Define a field of space; 2) Define a scalar potential that is a function of position at each point in this field; 3) Define a field constant that is constant over the whole field; 4) Define the field potential as the product of the field constant and the scalar potential; 5) Define a force as the negative gradient of the field potential; 6) Define the field strength as the force per unit field constant. The field strength is also the negative gradient of the scalar potential, or the gradient vector. If it is assumed that the field constant is a quantity that is conserved by a field, then forces may be derived for each of these conserved quantities. This approach is just the inverse of current practice. Several different forces may be derived that conform to the same six steps above, based upon the conservation of mass, mass flux, momentum, angular momentum, spring constant, energy, quantum, et al.