4. Field-effect relationship

4.1. Considerations on the method
4.2. The field of electric effects
4.2.1. The field x of a loaded conductive sphere
4.3. The electrostatic force
4.3.1. Electrostatic force between loaded conductive spheres

4.1. Considerations on the method:

        An area in space is the headquarters of a field when it is possible to characterize in it a physical property given by a function of position and time [32]. This definition involves a mensuration process that for interaction field implies the acceptance of the existence of an effect on a test object. It is important to notice that for the same field the observed property can be different if the test objects are different. With this restriction in mind and going back to the above-mentioned definition, we might conclude that the field is characterized by its effects, and not by its cause.

        What can we say about the method? When referring to the inherent difficulties of the elaboration of electromagnetic field theories, Eisntein commented: "The lack of a systematic method prevented us from getting to a solution." [33]

        In my opinion any method to be used in scientific theorization should have the following absolute rules:

1) not to despise confirmed experimental data;
2) not to fill theoretical gaps with controversial experimental concepts;
3) not to defend obsolete theories, regardless of their mathematical elegance and beauty;
4) not to save equations that have proved incompatible with experimentation, although they may appeal to us;
5) to make explicit the goals that theoretical researcher intends to reach in each stage of theorization;
6) to propitiate the necessary revisions of results obtained in previous stages;
7) to propitiate the development of general theories;
8) to propitiate conditions to endow the developed theories with internal coherence;
9) to loathe all and any prejudice;
10) to refuse any bias.

        Scientists generally agree, defend and emphasize these rules. Due to unknown reasons, they do not always follow them, as we saw in item 3 of this article.
        In field theories, the great step forward was given by Newton. Three hundred years after him, the decisive step is still to be taken, and most theoretical physicists of our century do not believe that such step can be taken. Schrdinger, De Broglie and Einstein are important exceptions to this rule; to quote Popper, for them "scientists should neither abandon the search for universal laws, nor the attempts of explaining any kind of event, starting from its causes." [op. cit. 22]
        Actually we know a lot about fields: on what they act, how they act and the consequences of these actions; and we know how to produce them. If we do not take into consideration the paradigms of ignorance, if we guide ourselves strictly by the rules presented above and if we focus the elementary causal agent of the field something we do miss we will certainly get to the foundations of a consistent field theory. After this stage and knowing the foundations, we can develop the first phase of the theory, that is, the deductive phase. Starting from this phase and knowing the cause although hypothetically we can evaluate its effects thus arriving at the field equations: this is the second phase, or analytic phase of the theory, which will the main theme of this item (4). If the theory is consistent, its equation will reveal a real surprise: "besides the field concept there will be no other concept concerning particles" since we chose to exclude the cause when defining the field.

        Let us now analyze the restriction we mentioned at the beginning of this item: the property that characterizes a field can differ if the test objects are different. This inconvenience can and should be avoided. For example, force is not always a good property to characterize a force field: its value only became a position function when refers to the same test object. In the case of electric field the artifice adopted by the classic theory is simple: E property is defined as the force per electric charge unit

in which q is given by Coloumb’s law.

        The artifice will be exclusively efficient if all the elements which are sensitive to the field can be imagined as one of the loaded spheres used in Coulomb’s experiment. A particle not presenting such property, i.e., that cannot be thought of as an electric charge, will present an anomalous behavior in the field under consideration. This anomaly is provoked by the bad characterization of the field rather than by properties inherent to the particle (hidden variables). There were countless experiments in this century trying to show an anomalous behavior of electrons when submitted to fields characterized by the 4.1 expression; and a collection of these anomalies can be found in any modern physics textbook.

        There are, however, some very uncommon conditions under which the electron simulates a classic behavior, as if it really possessed a q electric charge; and this will be the clue we are going to use together with 1 to 4 hypotheses in order to get into the mysterious world the elementary particles. We shall interpret these rare experimental occurrences, trying to establish a background so that we may get to the electron equation foreseen in hypothesis 3.