Copenhagen view

The challenges come from Refs. [1, 7, 8, 10]. The Copenhagen view on QM requires the existence of a classical macroscopic domain in order to explain the measurement process. Heisenberg uncertainty relations appear as the mathematical expression of a complementarity concept, quantifying the mutual disturbance that takes place in a simultaneous measurement of incompatible observables, say A and 6, that is, operators that do not commute. 

There is not a quantum jump in the description given above. The import of this situation can be appraised with respect to thesis 6 from Copenhagen view [3]. The physical situation is subtler. 

The present approach conflicts with Copenhagen view tenets quoted in Section 3.2. The concept of object is replaced by the elementary constitutive materials, viz. electron and nuclei sustaining quantum states. The parameters defining charge spin and mass enter those differential equations used to calculate model quantum states (time-independent eigenvalue Schrodinger equation or relativistic equations [5]). 

The conventional conceptual content of quantum mechanics was initiated by the Copenhagen School when it was recognized that one could express the linear Schrodinger wave mechanics [28] in terms of a probability calculus, whose solutions are represented with a Hilbert function space. Max Bom then interpreted the wave nature of matter in terms of a spatially distributed probability amplitude—a wave represented by a complex function—to accompany the material particle as it moves from one place to another. The Copenhagen view was then to define the basic nature of matter in terms of the measurement process, with an underlying probability calculus, wherein the probability densities (for locating the particles of matter/volume) are the real-number-valued moduli of the matter wave amplitudes. 

Werner Heisenberg (1901-1976 Nobel Prize for physics 1932) developed quantum mechanics, which allowed an accurate description of the atom. Together with his teacher and friend Niels Bohr, he elaborated the consequences in the "Copenhagen Interpretation" — a new world view. He found that the classical laws of physics are not valid at the atomic level. Coincidence and probability replaced cause and effect. According to the Heisenberg Uncertainty Principle, the location and momentum of atomic particles cannot be determined simultaneously. If the value of one is measured, the other is necessarily changed. 

The interminable discussions on the interpretation of quantum theory that followed the pioneering events are now considered to be of interest only to philosophers and historians, but not to physicists. In their view, finality had been reached on acceptance of the Copenhagen interpretation and the mathematical demonstration by John von Neumann of the impossibility of any alternative interpretation. The fact that theoretical chemists still have not managed to realize the initial promise of solving all chemical problems by quantum mechanics probably only means some lack of insight on the their part. 

H. A. Scheraga, Carlsberg Research Comm., 49, 1 (1984). Protein Structure and Function, from a Colloidal to a Molecular View (7th Linderstrom—Lang Lecture, Copenhagen, May 10, 1983). 

Fig. 16.7 (a) Schematic view of typical element of urban canopy - street canyon (b) Wind flow and pollution dispersion for the part of Copenhagen area... 

Figure 8 Widmanstatten pattern in a poUshed and etched section of the IlD iron meteorite, Carbo. 10 cm field of view. The brownish tear shaped troilite nodule to the left has acted as precipitation site for kamacite (Geological Museum, University of Copenhagen, specimen 1990.143).

Figure 3 The structural levels of proteins, exemplified by human insulin in the T6 form. (A) Primary structure residues 15-18 of human insulin B-chain, shown as sticks. (B) Secondary structure residues 8-20 of the B-chain form an a-helix, here depicted as a superposition of sticks, and a cartoon-representation. (C) Tertiary structure insulin A- and B-chains fold up to a monomer, which is assumed to be the active form, binding to the insulin receptor. Insulin can exist in different oligomeric forms, depending on formulation and protein concentration. (D) The Zn -stabilized hexamer form is shown. 2 Zn ions are bound per insulin hexamer (only one Zn2" "-ion is visible in this view). The hexamer is a trimer of dimmers. Figure based on pdb-file IMSO, produced in Pymol. Source Bente Vestergaard, Biostructural Research, Faculty of Pharmaceutical Sciences, University of Copenhagen.

Click the View Summary of Hits button. This opens a new window titled Summary of New Hits with Organism Vaccinia virus (Copenhagen), containing a table with four columns (see Note 10) (Fig. 1C). 

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