It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments. (shrink)

In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger during 1920–1927 are treated. From the formulation of quantum mechanics in 1925–1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory—formulated in fall 1926 by Dirac, London, and Jordan—Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in (...) September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of qnautum mechanics and of physical theory as such—formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930—were continued during the next decades. All these aspects are briefly summarized. (shrink)

SummaryA short exposition is given of the foundation of the causal description in classical physics and the failure of the principle of causality in coping with atomic phenomena. It is emphasized that the individuality of the quantum processes excludes a separation between a behaviour of the atomic objects and their interaction with the measuring instruments denning the conditions under which the phenomena appear. This circumstance forces us to recognize a novel relationship, conveniently termed complementarity, between empirical evidence obtained under different (...) experimental conditions. An appropriate tool for a complementary mode of description is provided by the quantum‐mechanical formalism which allows us to account for regularities of definite or statistical character beyond the grasp of classical physical explanation. – N. B. (shrink)

Quantum mechanics is generally regarded as the physical theory that is our best candidate for a fundamental and universal description of the physical world. The conceptual framework employed by this theory differs drastically from that of classical physics. Indeed, the transition from classical to quantum physics marks a genuine revolution in our understanding of the physical world.

— Niels Bohr, 19231 “There must be quite definite and clear grounds, why you repeatedly declare that one must interpret observations classically, which lie absolute ly in thei r essenc e. . . . It must belong to your deepest conviction—and I cannot understand on what you base it.”.

I develop a new analysis of Niels Bohr's Copenhagen interpretation of quantum mechanics by examining the development of his views from his earlier use of the correspondence principle in the so-called 'old quantum theory' to his articulation of the idea of complementarity in the context of the novel mathematical formalism of quantum mechanics. I argue that Bohr was motivated not by controversial and perhaps dispensable epistemological ideas---positivism or neo-Kantianism, for example---but by his own unique perspective on the difficulties of creating (...) a new working physics of the internal structure of the atom. Bohr's use of the correspondence principle in the old quantum theory was associated with an empirical methodology that used this principle as an epistemological bridge to connect empirical phenomena with quantum models. The application of the correspondence principle required that one determine the validity of the idealizations and approximations necessary for the judicious use of classical physics within quantum theory. Bohr's interpretation of the new quantum mechanics then focused on the largely unexamined ways in which the developing abstract mathematical formalism is given empirical content by precisely this process of approximation. Significant consistency between his later interpretive framework and his forms of argument with the correspondence principle indicate that complementarity is best understood as a relationship among the various approximations and idealizations that must be made when one connects otherwise meaningless quantum mechanical symbols to empirical situations or 'experimental arrangements' described using concepts from classical physics. We discover that this relationship is unavoidable not through any sort of a priori analysis of the priority of classical concepts, but because quantum mechanics incorporates the correspondence approach in the way in which it represents quantum properties with matrices of transition probabilities, the empirical meaning of which depend on the situation but in general are tied to the correspondence connection to the spectra. For Bohr, it is then the commutation relations, which arise from the formalism, which inform us of the complementary nature of this approximate representation of quantum properties via the classical equations through which we connect them to experiments. (shrink)