dorsal/arxiv
View SchemaProblems and Aspects of Energy-Driven Wavefunction Collapse Models
| Authors | Philip Pearle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310086 |
| URL | https://arxiv.org/abs/quant-ph/0310086 |
| DOI | 10.1103/PhysRevA.69.042106 |
Abstract
Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one case, a common particle position measuring situation, the apparatus evolves to a superposition of macroscopically distinguishable states (does not collapse to one of them as it should) because each such particle/apparatus/environment state has precisely the same energy spectrum. Second, assuming an experiment takes place involving collapse to one of two possible outcomes which is permanently recorded, it is shown in general that this can only happen in the unlikely case that the two apparatus states corresponding to the two outcomes have disjoint energy spectra. Next, the progressive narrowing of the energy spectrum due to the collapse mechanism is considered. This has the effect of broadening the time evolution of objects as the universe evolves. Two examples, one involving a precessing spin, the other involving creation of an excited state followed by its decay, are presented in the form of paradoxes. In both examples, the microscopic behavior predicted by standard quantum theory is significantly altered under energy-driven collapse, but this alteration is not observed by an apparatus when it is included in the quantum description. The resolution involves recognition that the statevector describing the apparatus does not collapse, but evolves to a superposition of macroscopically different states.
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"abstract": "Four problematic circumstances are considered, involving models which\ndescribe dynamical wavefunction collapse toward energy eigenstates, for which\nit is shown that wavefunction collapse of macroscopic objects does not work\nproperly. In one case, a common particle position measuring situation, the\napparatus evolves to a superposition of macroscopically distinguishable states\n(does not collapse to one of them as it should) because each such\nparticle/apparatus/environment state has precisely the same energy spectrum.\nSecond, assuming an experiment takes place involving collapse to one of two\npossible outcomes which is permanently recorded, it is shown in general that\nthis can only happen in the unlikely case that the two apparatus states\ncorresponding to the two outcomes have disjoint energy spectra. Next, the\nprogressive narrowing of the energy spectrum due to the collapse mechanism is\nconsidered. This has the effect of broadening the time evolution of objects as\nthe universe evolves. Two examples, one involving a precessing spin, the other\ninvolving creation of an excited state followed by its decay, are presented in\nthe form of paradoxes. In both examples, the microscopic behavior predicted by\nstandard quantum theory is significantly altered under energy-driven collapse,\nbut this alteration is not observed by an apparatus when it is included in the\nquantum description. The resolution involves recognition that the statevector\ndescribing the apparatus does not collapse, but evolves to a superposition of\nmacroscopically different states.",
"arxiv_id": "quant-ph/0310086",
"authors": [
"Philip Pearle"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.042106",
"title": "Problems and Aspects of Energy-Driven Wavefunction Collapse Models",
"url": "https://arxiv.org/abs/quant-ph/0310086"
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