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Process Studies

Collapse of the Quantum Wave Function

Pete A. Y. Gunter

Published Jan 1, 2009• 4 citations
Publisher

Abstract

Abstract The following introduction offers a broad survey of the history of quantum physics. It then outlines the position of each contributor in this Special Focus Section concerning the collapse of the quantum wavefunction and defines three important terms (Hubert space, Schrödinger’s cat, and decoherence) used in discussing this topic.

DOI
10.2307/44798491

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arXiv:2111.00337•Pisa University Press eBooks•Jan 1, 2023•0 citations
Abstract The following introduction offers a broad survey of the history of quantum physics. It then outlines the position of each contributor in this Special Focus Section concerning the collapse of the quantum wavefunction and defines three important terms (Hubert space, Schrödinger’s cat, and decoherence) used in discussing this topic.
The most discussed of ``live'' metaphors in physical sciences is that of the Schrödinger cat. Introduced in the early, but mature days of the new quantum theory, in 1935, the parable of the cat has provoked and enlivened debates on the meaning of the quantum theory, on the ontology of the quantum wavefunction, on the puzzle of the collapse of the wavefunction, on the meaning of quantum measurement, and on the boundary between the quantum world and the classical world. In this article, I will discuss these issues of the quantum theory focussing on various aspects of the metaphor of the Schrödinger cat.
Abstract Basic experimental evidence is sketched: the black body radiation spectrum, the photoeffect, Compton scattering and electron diffraction; the Bohr model of the atom. Quantum mechanics is reviewed using the Copenhagen interpretation: eigenstates, observables, hermitian operators and expectation values are explained. Wave-particle duality, Schrödinger’s equation, and expressions for particle density and current are described. The uncertainty principle, the collapse of the wavefunction, Schrödinger’s cat and the no-cloning theorem are discussed. Dirac delta functions and the usage of wavepackets are explained. An introduction to state vectors in Hilbert space and the bra-ket notation is given. Abstracts of special relativity and Lorentz invariants follow. Minimal electromagnetic coupling and the gauge transformations are explained.
The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave function collapse, for which Feynman hints to decoherence as a possible solution, is discussed. Finally, another topic is analyzed, concerning the role of the observer in a closed Universe. In this respect, Feynman's many-worlds characterization of Everett's approach at Chapel Hill is discussed, together with later contributions of his, including a kind of Schrödinger's cat paradox, which are scattered throughout the 1962-63 Lectures on Gravitation. Philosophical implications of Feynman's ideas in relation to foundational issues are also discussed.