dorsal/arxiv
View SchemaBetween classical and quantum
| Authors | N. P. Landsman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506082 |
| URL | https://arxiv.org/abs/quant-ph/0506082 |
Abstract
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. 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 h -> 0 of small Planck's constant (in a finite system), in the limit of a large system, and through decoherence and consistent histores. 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. We 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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"abstract": "The relationship between classical and quantum theory is of central\nimportance to the philosophy of physics, and any interpretation of quantum\nmechanics has to clarify it. Our discussion of this relationship is partly\nhistorical and conceptual, but mostly technical and mathematically rigorous,\nincluding over 500 references. On the assumption that quantum mechanics is\nuniversal and complete, we discuss three ways in which classical physics has so\nfar been believed to emerge from quantum physics, namely in the limit h -\u003e 0 of\nsmall Planck\u0027s constant (in a finite system), in the limit of a large system,\nand through decoherence and consistent histores. The first limit is closely\nrelated to modern quantization theory and microlocal analysis, whereas the\nsecond involves methods of C*-algebras and the concepts of superselection\nsectors and macroscopic observables. In these limits, the classical world does\nnot emerge as a sharply defined objective reality, but rather as an approximate\nappearance relative to certain \"classical\" states and observables. Decoherence\nsubsequently clarifies the role of such states, in that they are \"einselected\",\ni.e. robust against coupling to the environment. Furthermore, the nature of\nclassical observables is elucidated by the fact that they typically define\n(approximately) consistent sets of histories. We make the point that\nclassicality results from the elimination of certain states and observables\nfrom quantum theory. Thus the classical world is not created by observation (as\nHeisenberg once claimed), but rather by the lack of it.",
"arxiv_id": "quant-ph/0506082",
"authors": [
"N. P. Landsman"
],
"categories": [
"quant-ph"
],
"title": "Between classical and quantum",
"url": "https://arxiv.org/abs/quant-ph/0506082"
},
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