The Copenhagen Interpretation

13u Dhjstration of the Heisenberg uneertainty principle, (al) as function of coordi- 

In particular, for = x and B = px, if quantum mechanics is valid, one cannot measure the exact position and the exact momentum of a particle. When the precision with which x is measured increases, the particle s momentum has so wide a distribution that the error in determining px is huge, Fig. 1.13.  

In the 1920s and 1930s, Copenhagen for quantum mechanics was like Rome for catholics, and Bohr played the role of the president of the Quantum Faith Con- 

Bohr presented a philosophical interpretation of the world, which at its foundation had in a sense a non-reality of the world. 

According to Bohr, before a measurement on a particle is made, nothing can be said about the value of a given mechanical quantity, unless the wave function represents an eigenfunction of the operator of this mechanical quantity. Moreover, except in this case, the particle does not have any fixed value ol mechanical quantity at all. 

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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-... 

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. 

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. 

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. 

What we perceive to be physical reality is actually our cognitive construction of it. This cognitive construction may appear to be substantive, but the Copenhagen Interpretation of Quantum Mechanics leads directly to the conclusion that the physical world itself is not.9... 

There came a time when each model expanded too rapidly for scientists to keep track of all points of view and for the practitioners to reach a consensus interpretation. In the case of quantum theory the arguments were settled, to the satisfaction of none, on the authority of a few, and ordained as the Copenhagen interpretation. There is no written record to the details of this interpretation, which to this day, remains open to the formulation that best suits individual tastes. One of the authors who claimed responsibility for the interpretation (Heisenberg, 1955) states the purpose of the paper to... 

However, the problem of A in particle physics remains. It can be traced back to the concept of massive indivisible point particles with infinite self-energy and self-field - the basic premise of field theories based on the Copenhagen interpretation of quantum mechanics. As recollected by one pioneer... 

The months which followed [... ] were a time of the most intensive work in Copenhagen, from which there finally emerged what is called the "Copenhagen interpretation of quantum theory," [... ] BOHR intended to work the new simple pictures, obtained by wave mechanics, into the interpretation of the theory, while I for my part attempted to extend the physical significance. ... 

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