Copenhagen interpretation

The historical and philosophical aspects of the Copenhagen interpretation are more extensively discussed in J. Baggott (1992) The Meaning of Quantum Theory (Oxford University Press, Oxford). 

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 answer to this question depends on the chosen, underlying theory. According to the Copenhagen interpretation of quantum physics, the wavefunc-... 

This result indicates that the existence theta wave is made evident by the presence of the interference pattern. In the usual Copenhagen interpretation, the waves theta do not exist and therefore the expected result would be simple the one produced by the single source... 

In the Copenhagen interpretation of quantum theory, this standard (see Fig. 21) for the measurement cannot be changed at will since it is composed of sinus waves infinite in length. 

There are several reasons for this unsatisfactory state of affairs. Most important is perhars the different conceptual demands on theories of chemistry and physics respectively. In this instance there has been no effort to re-interpret mathematical quantum theory to satisfy the needs of chemistry. The physical, or Copenhagen, interpretation, which is essentially an ensemble theory, is simply not able to handle the individual elementary units needed to formulate a successful theory of chemical cohesion and interaction. Computational dexterity without some mechanistic basis does not constitute a theory. Equally unfortunate has been the dogmatic insistence of theoretical chemists to drag their outdated phenomenological notions into the formulation of a hybrid theory, neither classical nor quantum even to the point of discarding... 

The orthodox or Copenhagen interpretation of quantum theory originated with three seminal papers published in 1925-26 by Heisenberg, Born and Jordan and an independent paper by Dirac (1926) all of these are available in English (translation) in a single volume [13]. A detailed summary was published by Heisenberg [9]. The primary aim of these studies was to formulate a mathematical system for the mechanics of atomic and electronic motion, based entirely on relations between experimentally observable quantities. An immediate consequence of this stipulation was that the motion of electrons could no longer be described in terms of the familiar concepts of space and time, but rather in terms of state functions constructed from matrix elements that relate to the Fourier sums over observed spectroscopic frequencies. The procedure became known as matrix mechanics. 

The Copenhagen model is universally acknowledged as the ruling interpretation of quantum theory, although an authorized complete statement of the underlying principle does not appear to exist. In fact, such a statement is probably no longer needed as the Copenhagen interpretation, or orthodoxy, is so widely accepted as synonymous with quantum theory itself that, in ef-... 

This single item was originally referred to as the Copenhagen interpretation, which developed from there with each new argument against Schrodinger. 

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. 

It is interesting to note that the Gottingen school, who later developed matrix mechanics, followed the mathematical route, while Schrodinger linked his wave mechanics to a physical picture. Despite their mathematical equivalence as Sturm-Liouville problems, the two approaches have never been reconciled. It will be argued that Schrodinger s physical model had no room for classical particles, as later assumed in the Copenhagen interpretation of quantum mechanics. Rather than contemplate the wave alternative the Copenhagen orthodoxy preferred to disperse their point particles in a probability density and to dress up their interpretation with the uncertainty principle and a quantum measurement problem to avoid any wave structure. 

A central problem is posed by the so-called interpretation of QM [9]. Thus, for instance, Ballentine [10] discusses two cases (1) The Copenhagen Interpretation and (2) The Statistical Interpretation. 

The concept of measurement disturbance should apply to cases given in Eqs. (7 and 8), while Eq. (6) refers to the preparation step, de Muynck concludes [8] that "[w]ith no proper distinction between preparation and measurement the Copenhagen interpretation was bound to amalgamate the two forms of complementarity, thus interpreting the Heisenberg-Kennard-Robertson uncertainty as a property of (joint) measurement." Statements such as these may appear to be unclear, but this is the state of the matter as given by de Muynck. 

In 1935 Erwin SchrOdinger published an essay questioning whether strict adherence to the Copenhagen interpretation can cause the weirdness of the quantum world to creep into everyday reality. He speculated on how the principle of superposition, which is so fundamental for the quantum-mechanical behavior of microscopic systems, might possibly affect the behavior of a large-scale object. 

Copenhagen interpretation, quantum mechanics, 266 Coulomb s law, 94 Crystal field theory, transition metal complexes, 149-152 Curvilinear coordinates, overview, 80, 86-88... 

This can be generalized for any number of contributing states. According to the Copenhagen interpretation, the wavefunction for state ih can, under certain circumstances, collapse to one of the component states lor 2> with a probability c p or c2p, respectively. When this happens, all other components of the superposition essentially disappear. 

---