2.1 Physics, mathematics and theorization:

We can state — with some inaccuracies — that for the physicist field means what functions mean for the mathematician and since field is a function we could think that there is no distinction between Physics and Mathematics at least in this domain. There is a certain fallacy in this way of thinking: for the physicist field is more than a function — it is a function generated by another field or by natural principle; and it is a function generating effects. The quantification of the cause-field and field-effect relationships belongs to experimental Physics; the rest are theoretical Physics, Philosophy of the Sciences or pure Mathematics — themes we cannot always distinguish very well since there is a lot of artificialism in them.

Changing experimental information into a mathematical language implies the acceptance of some hypotheses that — if at all plausible — converge to a more general solution (theory). The following hypotheses come from the reinterpretation of successful experiments exhaustibly confirmed in the past 200 years — they are the same experiments that support classic electromagnetism and most part of modern Physics. Through this text I hope to make clear this interdependence, as well to reinforce the fact that the mathematical language in Maxwell’s theory is entirely correct, although irreducible to the universe of elementary particles.

2.2 Hypotheses:

As we shall see, hypotheses 1 to 4 constitute a necessary and sufficient group of statements set out to establish an electromagnetic theory in agreement with physical reality. Any additional statement should come directly from experimental data. In this sense we shall not think of variants and invariants as concepts like mass, time and speed, etc. For example: saying that the electromagnetic information spread a speed c, I want simply to say that they spread within this speed c. No supposition will be made about the possible performance of c that does not come directly from an experiment. On the other hand and to avoid misunderstanding I shall use the symbols x and b for the vectorial fields related to those which I name electromagnetic fields, and E and B for the classic electric and magnetic fields. The transformation from x into b, or vice versa, shall never be admitted — if so, it will be a consequence of the theory. In any case, and as we shall see, the group (x, b) is very different from the group (E,B ).

In the following chapters I shall use the operational language used for hypotheses 1 to 4. It would be interesting, however, to justify them physically. So, in the comments below I shall refer to the electron as an element of the electron-proton pair; and although electrons and protons differ substantially from other properties strange to electromagnetism, I shall maintain this rule in the following chapters.

2.3 Comments on H-1:

The expression mathematical electron of H-1 is not casual: it attracts the attention to essential aspects to the development of the theory to the detriment of other not less important aspects but with a physical meaning intimately related to the properties of the former ones. Among the latter ones we can mention the inner structure of the electron and also a presumably constant K parameter.

After all, is K constant or not? We could simply say that K is an arbitrary constant -- this would not affect the theory itself. As an arbitrary constant, we could endow it with a convenient value: one, for example. We shall see, however, that this is not the most convenient attitude from the physical point of view. It would be interesting to leave a degree of freedom in the relationship that defines w, and that will be useful under certain circumstances. So, K will be constant if and when we want it to, so long as we respect the experimental physical rules.

Unlike the one adopted by classic electromagnetism, it is a direct consequence of H-1:

2.4 Comments on H-2 :

The hypotheses from 1 to 3, as we shall see in the next chapter, form a group and as such they will be analyzed in due time. In this group, Hypothesis H-2 works as a bridge between H-1 and H-3, that could be omitted in a preliminary study. There are, however, some aspects inherent to hypotheses 2 which are important to the development of the theory and whose analysis should not be postponed regardless of its length.

What do electromagnetic information mean? What is their physical nature? The answer is not easy but I would dare say that any similarity to what has been traditionally called hidden variants of modern Physics might not be just a coincidence. Classical Physics can be reduced to fundamental concepts such as space, time, matter, and movement. The information are free from such reductionism: as they are emitted (H-2), they can be regarded as autocthonous. "Flow" is an inclusive term but it can always be thought as something flowing or running through a real or imaginary limit: a stream, the bunch of bullets shot by a machine-gun, sound, light or volcano lava — or even humanity — flowing through history. The ancient world associated it to movement, time, dynamics and evolution. Heraclitus thought that flow was essential to existence [8]; Aristotle associated flow to a cause: the act to the potency; and Epicurus proposed the association among Democritus’s atomism, the aleatory nature inherent to Heraclitus’s ideas, and the casual explanation proposed by Aristotle to conclude that mortality elapses from immortality: form remains although substance changes [9].

In field Physics there appears a new concept: flow without matter. Real or imaginary, concrete or abstract, the truth is that if a field does exist something can flow. It can go through vacuum and molecules, it deletes and has no respect for the infinite. It does not a medium to spread: in fact, ether does not exist. Space is its site; field is its existence. Emptiness is its nature.

A field can be modified, and when such modification occurs it transports energy; and a stationary field can be imagined as energy located in space. But energy, even the potential one, is something that flows, if we admit it can carry out an action. How can something be located and flow at the same time? In fact, there is a duality which is intrinsic to the field concept which could be solved if we should accept the idea of an ether of energy, the site of something immaterial that spreads and manifests itself locally as energy: materializing itself when observed, to use an expression that would please a realistic physicist of our century, without being totally opposite to the orthodox interpretation of Quantitative Physics. Let us quote the thought a great scientist and philosopher of science:

It is inconceivable that inanimate gross matter, without the mediation of something immaterial, might affect some other matter with no mutual contact, as it should happen if gravitation (in the sense proposed by Epicurus) were essential and inherent to matter. This is one of the reasons why I do not wish innate gravity to be attributed to me. For me it is totally absurd that gravitation should be innate, inherent and essential to matter, so that a body might act upon another body from a distance, through vacuum, without the mediation of something else, through which its action and force should be transported from one to the other; it is so absurd that I believe no man with philosophical questions in mind might believe it. Gravity must be caused by an agent constantly acting according to certain laws; but I should let my readers decide whether such agent is material or immaterial {Newton [10]}

With these words, Newton chooses an emission theory. But what kind of emission could it be? Of something immaterial?

The question raised by Newton has not been solved yet. My readers will decide whether such something which is neither matter nor energy but can exert some kind of effect does exist. But as we are going to mention it several times, it should be given a name: in accordance with its action I shall call it information — electromagnetic, gravitational, etc.

In Physics it is important to make a distinction between certain akin concepts. Beginners traditionally misunderstand the difference between heat and temperature in terms of thermodynamics. It is equally common to think that what flows in a speed field is speed itself. Reasoning in terms of field we can consider heat as the entity that flows in a temperature field. Speed field is little more complex or maybe a little more known. In this case, what flows can be regarded from several points of view: outflow or fluid volume that crosses a surface in the unit of time; mass corresponding to the considered volume; matter amount also corresponding to the considered volume and expressed, for examples, as a number of elementary particles. For each point of view, a different number that represents the same thing. We can also think what flows not in terms of current but of the degree of freedom and cohesion between the molecules in the fluid. Thus, we have a momentum flow spreading in a perpendicular way to its own direction: it is a flow generating another flow; or better, it is a tensorial field generating a vectorial one.

As we have seen, what we have in a temperature field is a heat flow; what flows in a speed field is called an outflow or a momentum flow. What about the electromagnetic field? What is the entity flowing in an electromagnetic field? I shall call it electromagnetic information, which may exist or not. If it exists it may be important or not. What matters is noticing that the stationary electromagnetic field does not spread, just like heat is not temperature. As a consequence the information I refer to is not an electromagnetic wave, although it transmits information.

2.5 Comments on H- 3:

From the physical point of view, hypothesis 3 characterizes the A field as a frozen image at the time of the electromagnetic information flow; it also allows a great number of suppositions such as: Can this image induce us to characterize mensurations: In fact, it translates the content in H-2 into a mathematical language. Thus, the expression "electron equation" is quite suggestive: the electron manifests its existence through its field. The physical mathematical relationship can be translated by the following statement:

The expression mathematical radius is symbolic and should not be confused with physical radius, since we have not made any suppositions upon the electron form. Anyway, and since we accept the idea of the electron impenetrability, the non-definition of A inside the electron shall not be harmful: it will always be possible to go from any P point to any Q point through a polygonal contained in the domain of the A function, and the P and Q extremities.

The A field is nothing else but field of information De Broglie dreamed of; it is a field that dictates other fields and, therefore, contains the Bohm’s superimplicit order [11]; and in its inner structure it also contains the classic potential fields: electric potential (scalar) e potential vector (magnetic).

2.6 Comments on H-4:

Hypothesis 4 (H-4) completes the cause-effect relationship — shown in figure 1 — due to the admission of an element that is sensitive to the A field and of the same electromagnetic nature of the element generating the field. The physical meaning becomes immediate: retroaction mechanisms become possible, that is, we can think of action-reaction phenomena; still, there appears the idea of permanent communication that brings to our mind the philosophical concept of the interlined Universe. We should also mention the need of a second symmetry break. The first one is inherent to Hypotheses 1-3: an asymmetric structure (H-1) generating (H-2) a field (H-3). From Hypothesis 4 we may realize that this morphogenetic field is going to act upon the form or inner structure of another electron. However, this is not enough to allow us to talk about a new symmetry break, but we can think — in terms of physical reality — about the transcendental importance of the double electron-proton existence.

From this viewpoint, Hypothesis 4 guarantees the mensuration of the A field through the observation of the way a test electron behaves in such field.

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