A scientific law always applies to a physical system under repeated conditions, and it implies that there is a causal relationship affecting the elements of the system. Factual and well-supported claims such as „mercury is liquid at standard temperature and pressure“ are considered too specific to be considered scientific law. A central problem in the philosophy of science, which dates back to David Hume, is the distinction between causal relations (as implicit by laws) and principles arising from constant conjunction. [6] A type 1 physical law or objective model is a constant relationship between two or more properties of a physical entity. In principle, each of these models can be conceptualized in different ways, i.e. as alternative type 2 laws. The history of theoretical physics is largely a consequence of type 2 laws. Each of these two is intended to represent a more accurate representation of the corresponding objective model or type 1 law, which is considered constant and, in particular, unaffected by human efforts to grasp. Similarly, the history of technology is, to some extent, a consequence of Type 3 laws or law-based rules of action, of which there are at least two for each Type 2 law. As for type 4 laws or laws, they are of two types: scientific and philosophical. The general principle of covariance is of the first type, while the assumption that all events are legitimate is a philosophical thesis.
Unlike the first, the veracity of which can be verified, the principle of legality is irrefutable. The exact formulation of what is now recognized as modern and valid statements of the laws of nature dates back to the 17th century in Europe, with the beginning of precise experimentation and the development of advanced forms of mathematics. During this period, natural philosophers such as Isaac Newton (1642-1727) were influenced by a religious view derived from medieval concepts of divine law that assumed that God had established absolute, universal, and immutable physical laws. [21] [22] In chapter 7 of Le Monde, René Descartes (1596-1650) describes „nature“ as matter itself, immutable as created by God, so that the changes in part „are attributable to nature. The rules by which these changes take place are what I call the „laws of nature.“ [23] The modern scientific method that was taking shape at the time (with Francis Bacon (1561-1626) and Galileo (1564-1642)) contributed to a tendency to separate science from theology, with minimal speculation about metaphysics and ethics. (Natural law in the political sense, conceived as universal (i.e. separate from sectarian religion and coincidences of place), was also elaborated during this period by scholars such as Grotius (1583-1645), Spinoza (1632-1677) and Hobbes (1588-1679). One paradigm of such limitation is that of the rigorous application of Feshbach`s oft-cited formalism, which explains the emergence and effect of resonances in nuclear reactions [2]. The faithful implementation of this formalism with regard to the use of well-defined projection operators on the resonance states of atomic systems was first demonstrated in 1965 by O“ Malley and Geltman [3a], but only for certain low resonance states of two-electron atoms. Subsequent work in this direction for two-electron systems investigated aspects of high computational accuracy, e.g.
Ref. [3b]. However, as the authors of these papers pointed out in the 1960s and early 1970s, this theory-based method is valid and practicable only for two-electron systems, since the target states are precisely known, the properties of the projection operators are strictly fulfilled, and the computational algorithm conforms to formalism. In order to circumvent the intrinsic requirements of the Feshbach scattering formalism regarding its extension to systems with more than two electrons, modifications in the sense of „quasi-projection operators“ were advanced in the 1980s and applied to the deepest resonances of the three electrons He− and Li [4]. A few years after the publications of Temkin and Bhatia [4a], Bylicki [5] penetrated into the essential theoretical aspects of this problem in conjunction with systematic calculations at three-electron resonances of He. For example, he paid attention to the choice of orbital orthogonality conditions when defining projection operators on open and closed channels – a practical approximation that, as Bylicki pointed out, in the polyelectronic theory of Ref.
