Classical ideas, failure

As a cultural activity this harsh discipline of quantum physics has been a failure. The layman continues to ask about the meaning of things and an occasional heretic, such as David Bohm [60], keeps the idea of an intelligible quantum reality alive. The quest for an electronic structure must be conducted in this spirit one can scarcely expect a discipline based on the electron as a zero-dimensional point to reveal its structure. However, despite Dirac s initial neglect of dimensional properties, he found a finite classical... 

Although the Bohr theory satisfactorily explained the spectra of hydrogen and of other species containing one electron (He, Li +, etc.) the wavelengths in the observed spectra of more complex species could not be calculated. Bohr s assumption of circular orbits was modified in 1916 by Arnold Sommerfeld (1868-1951), who assumed elliptical orbits. Even so, the Bohr approach was doomed to failure, because it modified classical mechanics to solve a problem that could not be solved by classical mechanics. It was a contrived solution. This failure of classical mechanics set the stage for the development of a new physics, quantum mechanics, to deal with small particles. The Bohr theory, however, did introduce the ideas that only certain energy levels are possible, that these energy levels are... 

If, contrary to the order of historical development, we have discussed the quantum theory of the atom before quantum statistics, we have our reasons. In the first place, the failure of- the classical theory displays itself in atomic mechanics—for instance, in the explanation of line spectra or the diffraction of electrons—even more immediately than in the attempts to fit the law of radiation into the frame of classical physics. In the second place, it is an advantage to understand the mechanism of the individual particles and the elementary processes before proceeding to set up a system of statistics based upon the quantum idea. 

Where complex properties occur in living systems, as for example in chaotic cardiac arrhythmias, they are characteristic of pathological failure of the normal controls— in this case in some kinds of heart disease—not of health. Even at the level of an individual enzyme, the enzyme peroxidase from horseradishes, an example of chaotic behavior has been known for many years, but we have no idea how its properties benefit the horseradish, and they contribute nothing to our present understanding of how metabolic systems are controlled in general. The sort of positive feedback loops that account for the complex behavior of economic systems, political relations, and indeed some aspects of biology such as the extravagant overdevelopment of the peacock s tail, are conspicuously absent from the major pathways in the metabolic economy. There is no reason, therefore, to see any contradiction in the claim that classical economic theory works much better in metabolism than it does in the domain in which it was developed. 

This has led many researchers to posmlate a simple shear stress criterion for failure. This idea persists to this day despite some early analysis, such as that of Goland and Reissner who used classical mechanics of material concepts to demonstrate that the joint includes shear, bending, and cleavage stresses [5], This is more recently substantiated by several numerical analyses, some of which are cited in [1]. 

In the preceding sections the so-called classical methods for estimating reliability data from observed lifetimes and failure frequencies were treated. It was shown as well how the corresponding confidence intervals are determined. All procedures were based on the frequentist concept of statistics. Its underlying idea is the probability expressed as the limit of a relative frequency, i.e. 

The methods of MM are devoid of this failure since electron correlation effects are implicitly included in the atom-atom potentials . However, these methods are classical by definition and do not describe the quantum effects, which are essential in the overwhelming majority of problems, in fact in all the problems in which the electronic states should be considered explicitly. These considerations lead directly to the idea to separate the molecular system in two (or more) regions in such a way as to find the quantum effects taking place overwhelmingly in only one of them, while the other regions could be considered by classical methods. The QM/MM approaches are based on this idea. 

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