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Foundations of Quantum Mechanics, an Empiricist Approach

Willem M. de Muynck

Published Jan 1, 2004• 111 citations
Publisher

Abstract

xi 4.5.24.5.3The double-slit experiment The microscope 4.6 Meaning of the 'complementarity' concept 4.6.1 4.6.24.6.34.6.44.6.5 4.6.6 4.6.7 Two meanings of 'to determine' Heisenberg's disturbance theory of measurement Complementarity according to Bohr Particle-wave duality Parallel and circular complementarity Complementarity and the projection postulate Complementarity and consciousness 4.7 Critique of the complementarity principle Einstein Margenau Ballentine Recent developments Complementarity and empiricist interpretation The Einstein-Podolsky-Rosen problem 6 Individual-particle and ensemble interpretations of quantum mechanics 275 6.

DOI
10.1007/0-306-48047-6

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xi 4.5.24.5.3The double-slit experiment The microscope 4.6 Meaning of the 'complementarity' concept 4.6.1 4.6.24.6.34.6.44.6.5 4.6.6 4.6.7 Two meanings of 'to determine' Heisenberg's disturbance theory of measurement Complementarity according to Bohr Particle-wave duality Parallel and circular complementarity Complementarity and the projection postulate Complementarity and consciousness 4.7 Critique of the complementarity principle Einstein Margenau Ballentine Recent developments Complementarity and empiricist interpretation The Einstein-Podolsky-Rosen problem 6 Individual-particle and ensemble interpretations of quantum mechanics 275 6.
A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynmann called the ``central mystery'' and the ``only mystery'' of quantum mechanics, leading to an interpretation of complementarity in which a `wave {\em and} particle' description rather than a `wave {\em or} particle' description is valid for the {\em same} experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different from Bohr's but is consistent with the von Neumann formulation as well as some more recent interpretations of quantum mechanics.
A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynman called the “central mystery” and the “only mystery”of quantum mechanics, leading to an interpretation of complementarity in which and description rather than a wave or particle' description is valid for the same experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different from Bohr's but is consistent with the von Neumann formulation as well as some more recent interpretations of quantum mechanics.
The interesting double-prism experiment of Ghose, Home, and Agarwal 5) has been suggested 5, 8, 16, 7, 6) as a challenge to Bohr´s views of complementarity. With the linguistic complementarity 14) as a general notion of complementarity, we analyze Bohr´s views of complementarity. We find that a careful formulation of Bohr´s wave-particle complementarity, with an explicit characterization of measurability as a particular low-level kind of quantum theoretical inferribility, is in fact not confronted by the double-prism experiment. Much less is the outcome a challenge to Bohr´s primary view of complementarity, namely as a tension between definability and observability in a quantum mechanical observation language. This primary view of Bohr, which is visible already in his Como paper 1), is a general formulation of quantum mechanical complementarity. Although it connects well to the subsequent metamathematical development of the wider linguistic complementarity, as a tension between describability and interpretability in a language, it is today surprisingly seldom referred to in quantum mechanical texts. Rather, discussions of the role of complementarity for the interpretability problem for quantum theory tend to focus on Bohr´s view of complementarity in terms of phenomena, which he conceived in his later discussions with Einstein (and which appears less clear than Bohr´s primary view of complementarity). The hierarchical structuring of quantum theory which is suggested in our analysis of the double-prism experiment, and in the analysis of complementarity in terms of phenomena, is of interest also for the general interpretability problem for quantum theory, and for questions about a quantum mechanical reality.
Preface to the 2nd edition. Preface. Acknowledgements. Reality in the quantum world: The quantum revolutions External reality The potential barrier and the breakdown of determinism The experimental challenge to reality Summary of chapter one. Quantum theory: The description of a particle in quantum theory The wavefunction The potential barrier according to quantum mechanics Interference Other applications of quantum theory Summary of chapter two. Quantum theory and external reality: Review of the problem The ensemble interpretation of quantum mechanics The wavefunction as a measure of our knowledge The wavefunction as part of external reality Measurement in quantum theory Interference and macroscopic objects Can quantum mechanics be changed so that it will reduce wavefunctions? Summary of chapter three. Consciousness: The relevance of conscious observers: What is a conscious observer? Does wavefunction reduction require conscious observers? God as the conscious observer The many-worlds interpretation Summary of chapter four. Hidden variables and non-locality: Review of hidden-variable theories The pilot wave The Einstein-Podolsky-Rosen thought experiment Bell's theorem Experimental verification of the non-local predictions of quantum theory Can signals travel faster than light Summary of chapter five. The mysteries of the quantum world: Where are we now? Quantum theory and relativity Where do we go next? Early history and the Copenhagen interpretation A bibliography and some recent opinions A final plea for reality A last look at the wavefunction Conclusions. Recent developments: Models with explicit collapse The Bohm model Many worlds Time and quantum theory A peculiarly quantum measurement Locality. Appendices. Index.
Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.