The Copenhagen Interpretation


As we are approaching the end of the discussion of quantum mechanics in the Pre-War Years’ it is appropriate to try and summarise what might be said to be the prevailing opinion of this era, now known as the Copenhagen interpretation. The essential concepts forwarded within this interpretation were devised by Niels Bohr, Werner Heisenberg, Max Born, and others, in the years 1924–27, which we shall first summarise in terms of the following bullets:

  1. A quantum system is completely described by a wave function [ψ], representing an observer's ‘subjective’ knowledge of the system. This premise underpinned much of Heisenberg’s thinking.

  2. The description of nature is essentially probabilistic, where the probability of an event is related to the square of the amplitude of the wave function. This is generally attributed to Max Born's description of probability density.

  3. It is not possible to know the value of all the properties of the system at the same time. As such, those values not known with precision must be defined within the limits of probabilities. This statement aligns to Heisenberg's uncertainty principle.

  4.  Matter exhibits a wave–particle duality, as defined by deBroglie’s hypothesis.

  5. While the duality of wave-particles must be invoked to explain experimental results, the nature of this duality is constrained by the complementarity principle of Niels Bohr.

  6. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum. This general premise was one strongly supported by Niels Bohr.

  7. The quantum mechanical description of large systems will closely approximate the classical description as defined by the correspondence principle of Bohr and Heisenberg.

The inclusion of the word ‘subjective’ in the first bullet is often debated. However, as a broad generalisation, most people assume that the Copenhagen interpretation refutes the physical existence of the wave function, as such, it is assumed to be nothing more than a theoretical concept. Therefore, the ‘subjective’ view is that the wave function is merely a mathematical tool for calculating the probabilities within a quantum system, which might be verify by experimental data. However, there are some who argue for an ‘objective’ variant of the Copenhagen Interpretation, which allows for the existence of a ‘real’ wave function; although this latter position would not have been endorsed by Niels Bohr. According to Bohr's philosophy, science should focus on predicting the outcomes of experiments and, as a consequence, he considered any additional assumptions to be meta-physical rather than scientific. However, this position possibly led to a summation of the Copenhagen interpretation, which appears to be more philosophical than scientific:

"What cannot be observed does not exist”

However, subsequently, some have argued for a revision of the meaning of this summation as follows:

"What is observed certainly exists; about what is not observed we are still free to make suitable assumptions. We use that freedom to avoid paradoxes.”

Having already discussed deBroglie’s hypothesis, Heisenberg’s Uncertainty principle and Born’s probability density, we possibly need to outline what has been referred to as the ‘complementarity’ and ‘correspondence’ principles. Bohr's complementarity principle relates to the issue of the wave-particle duality of both light and matter, which Bohr described in the following terms, albeit slightly paraphrased:

"Complementarity implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear. As a result, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects."

However, the following indirect description of complementarity, taken from paper entitled ‘The Evolution of Physics’ by Albert Einstein and Leopold Infeld might better describe the general contradictions with the idea of wave-particle duality:

"But what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do."

In contrast, the correspondence principle simply highlights that the quantum formulations must reduce to some classical equivalence at some ‘appropriate’ limit. This might be quantified by making reference to the earlier comparison of the dispersion time of an electron and a 1 gram marble. In essence, without the imposition of any measurement, the electron can be described as a quantum system using Schrodinger’s wave equation, while the quantum state of 1 gram marble collapses and appears to remain within the remit of a classical description of a particle. Within this general outline, we might characterise the Copenhagen interpretation as one of the earliest and most commonly taught interpretations of quantum mechanics. It forwards the idea that quantum mechanics does not yield a description of an objective reality, but deals only with probabilities of observing or measuring various entities which align to neither a classical description of a wave or a particle. For within the quantum domain, the act of measurement causes the set of probabilities to immediately assume only one of many possible values, which has subsequently been described in terms of the wave function collapse. However, given that this interpretation was reached over 90 years ago, we might wish to table a few questions for possible consideration in the next section of discussion covering the ‘Post-War Years’:

Did this interpretation reflect science or philosophy?
Does it still reflect the general consensus in the present era?

While the scope of the questions above are really for the next section, it was clear from the outset that not everyone agreed with the Copenhagen interpretation, especially in light of the following assertion of Heisenberg and Born at the Solvay Congress of 1927:

We regard quantum mechanics as a complete theory for which the fundamental physical and mathematical hypotheses are no longer susceptible of modification.

At this time, Einstein and Schrödinger were among the most notable dissenters, who never fully accepted the Copenhagen interpretation. Einstein in particular  became increasingly dissatisfied with the reliance upon probabilities, but possibly more fundamentally,  he philosophically disagreed with the assumption that physical existence might be dependent on an observer and that the motions of particles could never be precisely described. In this context, Einstein viewed quantum mechanics as incomplete in that it could only offered a statistical approximation of physical reality.