von Prof. Dr. Ulrich Herkenrath, Dr. med. Gerd Helmecke
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4. März 2022
If the universe as a whole is modeled and studied, the principal problem arises that it cannot be included into a larger model or system, about which something as for structure, laws or evolution is known. The various limitations of perception of mankind and individual human beings reinforce the difficulties of creating such a model. One has to extrapolate models and laws which are appropriate and valid for “subsystems” to design a maximal model for the universe as a whole. The first question is which models and laws are appropriate for such an extrapolation, the next one is how the extrapolation should be performed. In science the extrapolation of models and laws from a domain, in which their validity can be assured either by experience or by experiments, to a much larger domain, generally leads to delicate questions as to its admissibility. Since mathematics offers the keys to deal with science and to explain natural reality, extrapolations are performed via or by means of mathematical models. In general these models can be extrapolated to any extent or “up to infinity” according to the rules of mathematics. But if one wants to learn about natural reality, the question remains, whether an extrapolated mathematical model corresponds to a phenomenon existing in natural reality or not, i.e. whether a mathematical extrapolation is valid or admissible with regard to natural reality. Especially in the context of “infinity”, i.e. “infinitely large or small” (infinitesimal magnitudes e.g.), the problems of extrapolation reach their peak. With respect to the problem of admissible extrapolations or of limited admissibility of theoretical or mathematical models and laws, we point out three basic reasons for inadmissible extrapolation: First, the validity of a model may be restricted with respect to various aspects of the phenomenon to be modeled, i.e. some aspects are modeled appropriately, others not. As a classical example we mention the models for light, wave or particle. Another example is induced by the stochastic process of Brownian motion which represents the usual mathematical model for the motion of a small particle in a liquid. As is well-known, all paths of this process are almost everywhere non-differentiable, hence a velocity of the particle cannot be derived from this model. Of course, the velocity of the particle can be explained by means of a different model. Second, the right, true model respectively law can perhaps not be determined by observation or experiment because of the natural restrictions in the perception of human beings. The restrictions are either caused by the lack of appropriate technical instruments for observation or experimentation, or they are brought about by the observable range of the corresponding phenomena. Starting from a smaller range of observation, which is under control, and going to a larger one, there may be a change in the structure of the model or law. Up to some time in the past mankind had not been able to find out the laws of relativistic mechanics, but only those of “classical” mechanics. As further examples we mention some physicists’ doubt in our days that the well-known law of gravitation is correct over any wide range in the universe and Newton's second law is correct under any circumstances, cf. Milgrom (2002). Maybe the true laws applicable to the whole universe have not been found up to now, because of our limited capacity of observation. Third, necessary parameters for the evaluation or application of a certain law of nature possibly are not measured correctly. For example the law of gravitation in its known form may induce misleadings, because distances are not measured correctly. If inadmissible extrapolations are performed, they will provoke misleadings, contradictions, bizarre phenomena. On the level of mathematical models there appear so-called singularities, which in some sense represent the concentrated rest of unaccountable or contradictory facts and insufficiencies. Again, we mention some examples demonstrating these effects: The seeming possibility of time travelling (in the strict sense); a statement like “The effect precedes the cause”; the phenomenon of Dark Matter which is possibly caused by applying incorrectly the known law of gravitation or a false law; a statement like “There is a multitude of universes parallel to ours” without providing any empirical hint to that. With respect to the last statement the term “a multitude of universes” seems to be contradictory in itself already from the linguistic point of view. If one wants to build a model for the universe as a whole, in spite of the problems described, we propose to look out for general or basic principles, which are universally valid in nature. Therefore we are going to speak of foundations for a basic cosmos-model (abbreviated to BCM). We propose three principles or “Cosmic Laws”: - first, a universally observable law for structuring and restructuring natural reality; - second, a principle for ordering events in natural reality, a procedure that is necessary, if one wants to do and develop science claiming reliability; - third, an extension of the existing dimensionality, a mean that is necessary because of the insufficiencies and incompleteness of the existing models. The Cosmic Laws proposed by us do not constitute a scientific model for the universe as a whole. But they do represent foundations and are “test principles” to be applied to other complex models and theories, in order to find out, whether those are in accordance with the “Cosmic Laws”, and thus to avoid inadmissible extrapolations. The huge amount of strange particularities and contradictory competing models which can be found in the literature on astrophysics and cosmology (cf., e.g., Breuer 1993) is caused, as we think, mainly by inadmissible extrapolations. There may exist more than three Cosmic Laws. By collecting such laws and following our guideline referring to them when extrapolating models and laws to any extent, maybe to the whole universe, the situation could be improved.