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VI. Instead of Conclusion

Being just a mathematical introduction of some methods we use in different physical approaches, this essay hardly needs a conclusion other than the statement that it has been done. However, we feel compelled to give a short presentation of a physical problem to which we intend to apply this mathematical tool in the form presented above.

The Physics community became conscious, ever since the times of Mach, about the fact that the distant matter can act upon each body and, at least a part of this action can be labeled as inertia. The overwhelming majority of Physics works dealing with this subject adopt a vector model for inertia. We do not agree with this model, inasmuch as it involves nonlocal interactions and the place of what we designate as distant matter is usually vague, to say the least. Rather we think that if there is force involved in inertia, it stays in the background and is not revealed directly. More to the point one can think along the following scenario: let us consider a body at a certain point in Space. We find it just natural to think of the distant matter as acting simultaneously from all directions upon our body, thus inducing a state of stress that can be represented by a symmetric tensor, as stress is usually represented. One can further suppose that the action of distant matter is isotropic, so that our body feels a kind of average of influences. If these averages are taken as statistical averages of normal and shear stresses created by the distant matter at the location of the body, then it can be shown (Novozhilov, 1952) that they represent quantities proportional to the lengths of previously described normal and tangential components of our defined stress vector, with respect to the octahedral plane

The very same model can be adopted for the deformation of Space, only here we have to pay special attention to some preexisting curvature requirements. And just to round up logically this imagery, a constitutive law should exist relating the stresses induced in a body by the distant matter to the deformation as induced by the presence of that body in Space. As far as we can tell for now, this constitutive law has everything in common with the existence of electromagnetic fields (see Electromagnetic Fields, Constitutive Side of the Problem, this web page).

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