Wave function collapse: Difference between revisions

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The "Copenhagen" model espoused by Heisenberg and Bohr separated the quantum system from the classical measurement apparatus. In 1932

von Neumann took a more formal approach, developing an "ideal" measurement scheme<ref name=HartleQMCosmology>Hartle, James B. [https://arxiv.org/pdf/1805.12246.pdf "The quantum mechanics of cosmology."] Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. arXiv:1805.12246 (2018).</ref><ref name=SchlosshauerReview>{{Cite book |last=Schlosshauer |first=Maximilian |url=https://link.aps.org/doi/10.1103/RevModPhys.76.1267 |title=Decoherence, the measurement problem, and interpretations of quantum mechanics |date=2005-02-23 |volume=76 |pages=1267–1305 |language=en |doi=10.1103/RevModPhys.76.1267 |issn=0034-6861}}</ref>{{rp|1270|q=Note that von Neumann’s scheme is in sharp contrast to the Copenhagen interpretation, where measurement is not treated as a system-apparatus interaction described by the usual quantum-mechanical formalism, but instead as an independent component of the theory, to be represented entirely in fundamentally classical terms.}} that postulated that there were two processes of wave function change:

# The [[probability|probabilistic]], non-[[unitary transformation|unitary]], [[local realism|non-local]], discontinuous change brought about by observation and [[quantum measurement|measurement]] (state reduction or collapse).

# The [[deterministic]], unitary, continuous [[time evolution]] of an isolated system that obeys the [[Schrödinger equation]] (or a relativistic equivalent, i.e. the [[Dirac equation]]).

In 1957 [[Hugh Everett III]] proposed a model of quantum mechanics that dropped von Neumann's first postulate. Everett observed that the measurement apparatus was also a quantum system and its quantum interaction with the system under observation should determine the results. He proposed that the discontinuous change is instead a splitting of a wave function representing the universe.<ref name=SchlosshauerReview/>{{rp|1288}} While Everett's approach rekindlerekindled interest in foundational quantum mechanics, it left core issues unresolved. Two key issues relate to origin of the observed classical results: what causes quantum systems to appear classical and to resolve with the observed probabilities of the [[Born rule]].<ref name=SchlosshauerReview/>{{rp|1290}}<ref name=HartleQMCosmology/>{{rp|5}}

Beginning in 1970 [[H. Dieter Zeh]] sought a detailed [[quantum decoherence]] model for the discontinuous change without postulating collapse. Further work by [[Wojciech H. Zurek]] in 1980 lead eventually to a large number of papers on many aspects of the concept.<ref>{{Cite journal |last=Camilleri |first=Kristian |date=2009-12-01 |title=A history of entanglement: Decoherence and the interpretation problem |url=https://www.sciencedirect.com/science/article/pii/S1355219809000562 |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |series=On The History Of The Quantum |volume=40 |issue=4 |pages=290–302 |doi=10.1016/j.shpsb.2009.09.003 |issn=1355-2198}}</ref> Decoherence assumes that every quantum system interacts quantum mechanically with its environment and such interaction is not separable from the system, a concept called an "open system".<ref name=SchlosshauerReview/>{{rp|1273}} Decoherence has been shown to work very quickly and within a minimal environment, but as yet it has not succeeded in a providing a detailed model replacing the collapse postulate of orthodox quantum mechanics.<ref name=SchlosshauerReview/>{{rp|1302}}