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Heisenberg’s Uncertainty Principle and Bohr’s Complementarity (1927)

S. Brandt

Published Apr 22, 1992• 0 citations
Publisher

Abstract

Abstract In his memoirs Heisenberg reports on his first encounter with Einstein in April 1926. He had been invited to present his work on quantum mechanics in the prestigious Berlin colloquium and after the talk they walked together to Einstein’s apartment. Einstein began the conversation by criticizing Heisenberg’s postulate that quantum mechanics must be based exclusively on quantities which are in principle observable (Episode 37). Astonished, Heisenberg remarked that he thought, just that had been Einstein’s approach in special relativity when giving up the concept of absolute time, Einstein replied [1]: ‘Probably I did use this kind of reasoning, but it is nonsense all the same [… ] In reality the opposite happens. It is the theory which decides what we can observe.’

DOI
10.1093/oso/9780199544691.003.0043

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Abstract In his memoirs Heisenberg reports on his first encounter with Einstein in April 1926. He had been invited to present his work on quantum mechanics in the prestigious Berlin colloquium and after the talk they walked together to Einstein’s apartment. Einstein began the conversation by criticizing Heisenberg’s postulate that quantum mechanics must be based exclusively on quantities which are in principle observable (Episode 37). Astonished, Heisenberg remarked that he thought, just that had been Einstein’s approach in special relativity when giving up the concept of absolute time, Einstein replied [1]: ‘Probably I did use this kind of reasoning, but it is nonsense all the same [… ] In reality the opposite happens. It is the theory which decides what we can observe.’
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.
‘The new wave mechanics gave rise to the hope that an account of atomic phenomena might be obtained which would not differ essentially from that afforded by the classical theories of electricity and magnetism. Unfortunately, Bohr's statement in the following communication of the principles underlying the description of atomic phenomena gives little, if any, encouragement in this direction.’ This comment is to be found in the brief note prefaced by the editors of the British journal Nature to Niels Bohr's paper ‘The Quantum Postulate and the Recent Development of Atomic Theory’ in the supplement of 14 April 1928. The article in question is the famous paper which first introduced and defined the concept of ‘complementarity’ and outlined the basic points of what was to become known as the Copenhagen interpretation of quantum mechanics. In the paper, Bohr returned to the arguments contained in the paper discussed at the International Congress of Physicists held at Como in September 1927 to mark the centenary of the death of Alessandro Volta and published in the proceedings of the same congress. It was probably his conviction that the new viewpoint adopted in the description of nature fully expressed the theoretical and cognitive content of quantum physics coupled with his enthusiasm at having achieved ‘after many years of struggling in the dark […] the fulfilment of the old hopes’ that induced him to give his work broader and more prestigious circulation.
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.
The more scientists learned about the atom, the less categorical became the questions they put to nature. The uncertainty relation is a strict law of nature, which is in no way related to some imperfections of our devices. The uncertainty relation is directly opposed to intuition and everyday experience. Heisenberg explained the matter by discarding still another idealization of classical physics — the concept of observation. It turned out that in quantum mechanics it had to be revised, along with the concept of motion. The concepts of “phenomenon”, “measurement”, and “observation” are closely related to one another but they are by no means identical. Any measurement is essentially interaction between the instrument and the object to be studied. The principle that Bohr named complementarity is one of the most fundamental philosophical and scientific ideas of our time, which can only be compared to the principle of relativity and the concept of a physical field.
Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.
Abstract: Bohr’s interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr’s influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie’s had no reasonable foundation. But Bohr’s interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of explanations in the sciences (and not only the physical sciences). If it must be judged a failure today, it is not because of any internal inconsistency. Despite the expenditure of much effort, I have been unable to obtain a clear understanding of Bohr’s principle of complementarity (Einstein). Bohr’s point- and the central point of quantum mechanics- is that no elemen-