Quantum Chaos, Is There Any?

Ford, Joseph

doi:10.1142/9789814415729_0006

Cited by 9 publications

(2 citation statements)

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“…252 Arguments by Ford (1988) and others to the effect that quantum mechanics is wrong because it cannot give rise to chaos in its classical limit have to be discarded for the reasons given here. See also Belot & Earman (1997).…”

Section: Epilogue: Quantum Chaosmentioning

confidence: 99%

Between Classical and Quantum

Landsman¹

2007

Philosophy of Physics

104

140

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The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is Heisenberg's 'quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schrödinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail.On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit → 0 of small Planck's constant (in a finite system), in the limit N → ∞ of a large system with N degrees of freedom (at fixed ), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C * -algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain "classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are "einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories.This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it.

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Section: Epilogue: Quantum Chaosmentioning

confidence: 99%

Between Classical and Quantum

Landsman¹

2007

Philosophy of Physics

104

140

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“…Closely related to the discussion of the correspondence principle is the research area of quantum chaos and quantum chaology, where we ask whether chaotic behaviors seen in classical chaos can be derived within quantum physics. If the correspondence principle holds, then this is no brainer, but chaos actually presents some challenges to the correspondence principle, as suggested in [13,15,14].…”

Section: End-of-subsection Remarks With Emphasis On Quantum Chaosmentioning

confidence: 99%

The correspondence principle in light of holographic correspondence and the law of large numbers

Review

2023

Preprint

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The main philosophical lesson of holographic gravity is that spatiotemporal descriptions of a field theory may not be respected by observational reality. We apply this lesson to the correspondence principle, and then later justify the lesson (holographic correspondence) without necessitating such spatiotemporal deviations via the law of large numbers in statistics, applied to an average of n quantum measurements. Classical observables are considered to emerge as n approaches infinity. The averaging approach can be interpreted both as a generalization of Bohr's correspondence principle (large number limit) and Planck's correspondence principle (Planck's constant approaching zero). Holographic correspondence and the averaging approach are then re-analyzed in light of preceding works in the correspondence principle. A key consequential lesson is that we should not conflate the nature of fundamental theory observables with that of emergent theory observables, and once this confusion is avoided, the correspondence principle has a solid standing.

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Keeping Track of Chaos by Quantum-Nondemolition Measurements

Weigert

1992

Quantum Chaos — Quantum Measurement

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Quantum Chaos, Is There Any?

Cited by 9 publications

References 0 publications

Between Classical and Quantum

Between Classical and Quantum

The correspondence principle in light of holographic correspondence and the law of large numbers

Keeping Track of Chaos by Quantum-Nondemolition Measurements

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