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V. Conclusions

Classical Mechanics does not admit explicitly uncontrollable quantities. It rather declares them as given constants, measurable but not controllable. Such are the mass, charge, vacuum permittivity and permeability, etc. This basic philosophy has extended to all sciences of a classical nature. When it comes to the description of matter, the realm where a constitutive law must enter the stage, this philosophy extends the pure material parameters to the notion of state, thus mixing the issues. In order to put things in order, one way is to honestly recognize our impossibility of control over matter. Within the framework of constitutive laws this has an important impact: it decides the form of the deformation matrix as well as that of the stress matrix, in case a stress can be defined. Especially the definition of deformations, which involves only measurements, is characteristic to the evolution of a space metric from one of constant curvature.

The lesson to be learned here is that the Maxwell stress tensor is the only natural tensor containing uncontrollable quantities. This fact has a twofold impact on our thinking. First of all, the classical electromagnetism is formally legitimate. Thus if we reiterate Einstein’s question ”why light?” (Einstein, 1967), we can ask directly: because light is the primeval matter in existence. The fact that we know it better than anything else, etc., etc. comes only as a natural conclusion in the aftermath. A. H. Compton (Compton, 1922) emphasized the idea that according to all - although vague - definitions of the matter the electromagnetic field qualifies as matter. The present results can be taken as formal proof of that statement. The basis of this proof is not given by a definition of a philosophical nature, but by an engineering working tool: the constitutive relation between stresses and strains. Secondly, the mechanical thinking can take full advantage here: if the Maxwell tensor is the only legitimate form of a tensor representing either stresses or strains, then it is futile to search for some other forms when it comes to finding such things. All we have to do is to handle them correctly. Details of this handling aside, we can observe even for now that here a ‘dual’ character of electromagnetic field is involved, because this field ought to have the properties of radiation produced in mechanical processes, i.e. properties of heat. Thus, there is a subtle dif-ference between the thermal radiation and the light, even though they are usually considered the same. This seems to come forward lately in the explanation of parametric conversion thereby chal-lenging the fundamental values of Quantum Theory (Marshall, 2002)

A little digression: It is a delight to see a classic personality, like Trevor Marshall, taking side against Quantum Mechanics. The Reader is warmly invited to visit the web page of Trevor Marshall, the founder of Statistical Electrodynamics. While we completely agree with all points of view, philosophical and physical, expressed by Marshall, inasmuch as they regard the axiomatic approach of Quantum Mechanics, our general attitude is moderate. For nothing of what happens between Earth and Heaven is without a reason! Even Statistical Electrodynamics….

Let us close with a subject still hot, in spite of a century old debate: that of the General Relativity. It is well known how much discussion the Einstein field equations generated, mostly along lines regarding the tensor of the energy of the matter. First, the Space-Time is something very tangible, one can even say that it acts, for the field equations have nontrivial solutions in the absence of matter (De Sitter, 1918), this absence being defined by vanishing of the energy tensor. Then, it has been noticed that the absence of matter is not correctly defined, for according to the materialist concepts the electromagnetic field is actually matter, and the electromagnetic field fills the Space. Thus the idea appeared that the field equations, if they are to represent the gravitation phenomenon, must actually involve only the mass tensor, for only the mass generates gravitation (Fock, 1964).

Reserving the classification at length, of the theories around gravitation, to another occasion, we just notice that the only cases where the calculations succeeded in giving positive results, with impact mainly in Cosmology, are those where the energy tensor is either the Maxwell tensor or, if it is to represent the idea of bodily matter, of the form that we called before ‘equivalent of a vector’ (universal deformation of Coll and collaborators). From our point of view here the two cases are the same, for one tensor is a particular case of the other, and we can actually say that the Nature followed its selective course just … naturally. Indeed, the general idea here is just as simple as this: if one needs a constitutive law for the Space-Time, then the Einstein field equations give the most obvious constitutive law, when the measure of the deformation of the Space-Time is offered by the Ricci tensor. This constitutive law is entirely equivalent to the classical Hooke law from the case of small elastic deformations. One just has to exercise care as to what tensor energy one uses, for it has to be the one naturally reflecting the matter. As shown above this is a Maxwell type tensor.

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