Supplementary parameters theory

Bell s Inequalities provide a quantitative criterion to test some reasonable Supplementary Parameters Theories versus Quantum Mechanics. Thanks to Bell, the debate about the possibility of completing Quantum Mechanics by an underlying substructure has been brought into the experimental domain. 

The used formalism is deterministic. VJhen X is fixed, then the results of measurements A(X,a) and B(X,b) are certain, i.e. X determines the result. It might be thought that it is the reason for the conflict with Quantum Mechanics. But Belll and Clauser and Horne have exhibited Stochastic Supplementary Parameters Theories that are not deterministic, and which nevertheless lead to Bell s Inequalities. The deterministic character does not seem sufficient to lead to a conflict. ... 

As an abstract of this discussion, we can say that Bell s theorem states a conflict between Local Supplementary Parameters Theories and certain Quantum Mechanical predictions. It yields a quantitative criterion for this conflict, that will allow us to design sensitive experiments. 

Such a timing-experiment with variable analyzers would thus provide a test of Supplementary-Parameters-Theories, obeying Einstein s Causality, versus Quantum Mechanics. 

Although these assumptions are reasonable., let us mention that there exist supplementary-parameters theories that do not obey them. From the view point of supplementary-parameters theories, there is no way for experimentally testing these assumptions. ... 

Our last experiment (timing-experiment), as well as the previous ones, has some technical imperfections. Some loopholes thus remain open for the advocates of Supplementary-Parameters Theories obeying Einstein s Causality. Improved experiments will probably become feasible in the future but we already have an impressive agreement with Quantum Mechanics. Supplementary Parameters Theories obeying Einstein s Causality and compatible with our results appear somewhat artificial, since the experimental results would have to change dramatically (disagreement with Quantum Mechanics) with certain technical improvements(such as an increase of the efficiencies of the photomultipliers). ... 

Remark. Since Einstein spoke of "an element of the physical reality", some authors call these theories invoking supplementary parameters "Realistic Theories". ... 

The influence of atmospheric composition (and other factors) on climate can be studied by determining physical principles governing the climate and by constructing appopriate mathematical equations on the basis of these principles. As we have seen, the climate (radiation balance, temperature, circulation, etc.) is determined by the interaction of several processes. The parameters controlling these processes can be included in statistical or physico-mathematical equation systems which are called climate models. The solutions of these model equations provide the so-called climate theories. With the aid of these models, if they are formulated correctly, we can calculate theoretically the consequence of a given change in the parameters (e.g. an increase of COz level). Furthermore, it is also possible to include the effects of human activity in the models as supplementary mathematical relations. 

The CSA can be applied as a procedure supplementary to the standard SCF MO calculations. This is obvious in the case of the MO-resolved theory [48,89], but one can also use the SCF results to properly interpolate the input CS parameters, to reflect the actual valence-state of AIM [87], although some CS may be sensitive to the set of the AIM charges employed. 

It is concluded that while this method is certainly of value as a supplementary experimental method for preliminary electrode kinetic studies, at the present stage of development of its theory, it is not the best approach or even a good approach for the evaluation of kinetic parameters. 

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