Abstract

The compatibility of Coulomb Force with the special theory of relativity (STR), is a well know fact. But, any compatibility is not a must. Thus, the following question arises: Would there a more fundamental level, shaping the known structure of Coulomb Force, perhaps based on the foundations of the STR? Yes, indeed: It is that electric charges are Lorentz invariant, just like the speed of light, is. What seems so far ignored is the following. Not only that the constancy of the speed of light is, an empirical evidence, but the Lorentz invariance of electric charges, is too. These two facts do not seem to imply each other. Thus, both of them (as well as, perhaps the Lorenz invariance of similar entities, such as nuclear charges), must be considered concomitantly, in order to insure the Galilean principle of relativity with respect to all inertial frames of reference, which is in effect, the underlying postulate of the STR. Actually the constancy of the speed of light, does not appear to insure all alone, the validity of this principle, and this is why, exactly, Einstein cared to state the second postulate of the STR (regarding the sameness of the laws of nature with regards to all inertial frames of reference), although he did not make any use of it, throughout. Once we have the two evidences of concern (i.e. the Lorentz invariance of electric charges and that of the speed of light), then we can right away, mathematically derive the known Coulomb Force, though reigning between two static charges, exclusively. By the same token, the spatial dependency of Newton Force too, regarding two static masses, becomes a mathematical requirement based on  the STR, which seems to be something totally overlooked. So, both forces (still reigning between static, respectively, electric and gravitational charges only), are fundamental laws of nature, essentially imposed by the Galilean principle of relativity. In a subsequent article, however, we will show that, quite on the contrary to the general wisdom, neither Coulomb Force, nor Newton Force holds, if the ? electric or gravitational ? test charge in consideration, is in motion (the source charge being as usual, considered at rest, throughout). We show that, assuming the opposite (i.e. asserting that Coulomb Force, or Newton Force holds if the test charge, is in motion), constitutes a clear violation of the law of conservation of energy. Our approach removes the blockade toward a unification of fields, and the quantization of the gravitational field (hindered by the general theory of relativity).