One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.
One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.
Wonderful news from Copenhagen Heisenberg and Schrödinger invented mathematical formalisms that provided correct answers to all the various problems of (non-relativistic) quantum theory. It was Bohr who uncovered the underlying significance of the theory; in particular he showed how the profound conceptual difficulties encountered as the theory developed – the so-called wave–particle duality, the totally unclassical nature of the uncertainty principle – could be neutralised by a revision, or more accurately a generalisation, of our use of physical concepts. Such was the generally accepted view of things from soon after 1927, when Bohr first put forward his ideas on complementarity at an international meeting of physicists at Como, through the 1930s, when it was felt that Bohr destroyed Einstein's contrary opinions, and certainly up to the time of Bohr's death in 1962. Bohr's analysis is usually spoken of as the Copenhagen interpretation of quantum theory, though it is instructive to realise that such a term was frowned upon by those closest to Bohr, since it appears to suggest that the interpretation is just one among (conceivably) many. Let us examine, for example, the words of Léon Rosenfeld, Bohr's disciple and long-term collaborator, as expounded at a conference in 1957 [52]. Rosenfeld maintained that any idea of ‘interpreting a formalism’ was a ‘false problem’, that in a good theory, the ‘ordinary language (spiced with technical jargon for the sake of conciseness)’ in which it is described, is ‘ inseparably united … with whatever mathematical apparatus is necessary’, that ‘we are here not faced with a matter of choice between two possible languages or two possible interpretations, but with a rational language intimately connected with the formalism and adapted to it, on the one hand, and with rather wild, metaphysical speculations … on the other’.
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative
The founding fathers of quantum mechanics had already perceived the essence of the difficulties of quantum mechanics; today, after almost a century, the discussions are still lively and, if some very interesting new aspects have emerged, at a deeper level the questions have not changed so much. What is more recent, nevertheless, is a general change of attitude among physicists: until about 1970 or 1980, most physicists thought that the essential questions had been settled, and that “Bohr was right and proved his opponents to be wrong”. This was probably a consequence of the famous discussions between Bohr, Einstein, Schrödinger, Heisenberg, Pauli, de Broglie, and others (in particular at the Solvay meetings [1–3], where Bohr's point of view had successfully resisted Einstein's extremely clever attacks). The majority of physicists did not know the details of the arguments. They nevertheless thought that the standard “Copenhagen interpretation” had clearly emerged from the infancy of quantum mechanics as the only sensible attitude for good scientists. This interpretation includes the idea that modern physics must contain indeterminacy as an essential ingredient: it is fundamentally impossible to predict the outcome of single microscopical events; it is impossible to go beyond the formalism of the wave function (or its generalization, the state vector ∣ψ) and complete it.
Abstract One of the foundational principles of quantum mechanics is Heisenberg’s uncertainty relation. According to this relation, no one can measure both the position of a particle and how fast it is moving simultaneously no matter how precise the measuring instruments. Heisenberg’s uncertainty relation and the associated Bohr’s principle of complementarity are explained using simple examples. The idea that measurement disturbs the system is a source of the uncertainty. The philosophical question whether the uncertainty represents only our inability to measure the properties precisely or it has much deeper consequences related to the question of reality is also discussed.
From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π).
One of the most striking deviations of quantum mechanics from classical mechanics is that any measurement of a microscopic system involves the interaction with the measuring instruments. The interaction cannot be neglected and in fact leads to uncontrollable disturbance on the system. In 1927, Werner Karl Heisenberg in his celebrated paper established the quantitative expression for unavoidable momentum disturbance caused by any position measurement. The crucial word here is simultaneously. The uncertainty relation gives the lower bound on the product of the uncertainties of two pairs of variables. But it says nothing about the accuracy with which individual observables can be measured. The physical meaning of energy-time uncertainty is different from that of x-px uncertainty. Position and momentum are observables to which Hermitian operators are assigned and which are measured at a particular time. An important implication of the uncertainty principle is that quantum systems do follow classical trajectories which conflict with our everyday experience.