dorsal/arxiv
View SchemaQuantum and classical statistics of the electromagnetic zero-point field
| Authors | M. Ibison, B. Haisch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106097 |
| URL | https://arxiv.org/abs/quant-ph/0106097 |
| DOI | 10.1103/PhysRevA.54.2737 |
| Journal | Phys. Rev. A, vol. 54, pp. 2737-2744 (1996) |
Abstract
A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the EM quantum vacuum. We derive the distribution for the individual mode amplitudes in the ground-state as predicted by quantum field theory (QFT) and then carry out the same calculation for the classical ZPF analogue, showing that the distributions are only in approximate agreement, diverging as the density of k states decreases. We introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the EM vacuum of QED. Incorporated into SED, this new field is shown to give the correct (QM) distribution for the amplitude of the ground-state of a harmonic oscillator, suggesting the possibility of developing further successful correspondences between SED and QED.
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"abstract": "A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of\nquantum field theory has formed the basis for theoretical investigations in the\ndiscipline known as random or stochastic electrodynamics (SED) wherein quantum\nmeasurements are imitated by the introduction of a stochastic classical\nbackground EM field. Random EM fluctuations are assumed to provide\nperturbations which can mimic some quantum phenomena while retaining a purely\nclassical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb\nshift, spontaneous emission, the RMS radius of the harmonic oscillator, and the\nradius of the Bohr atom. This classical ZPF is represented as a homogeneous,\nisotropic ensemble of plane waves with fixed amplitudes and random phases.\nAveraging over the random phases is assumed to be equivalent to taking the\nground-state expectation values of the corresponding quantum operator. We\ndemonstrate that this is not precisely correct by examining the statistics of\nthe classical ZPF in contrast to that of the EM quantum vacuum. We derive the\ndistribution for the individual mode amplitudes in the ground-state as\npredicted by quantum field theory (QFT) and then carry out the same calculation\nfor the classical ZPF analogue, showing that the distributions are only in\napproximate agreement, diverging as the density of k states decreases. We\nintroduce an alternative classical ZPF with a different stochastic character,\nand demonstrate that it can exactly reproduce the statistics of the EM vacuum\nof QED. Incorporated into SED, this new field is shown to give the correct (QM)\ndistribution for the amplitude of the ground-state of a harmonic oscillator,\nsuggesting the possibility of developing further successful correspondences\nbetween SED and QED.",
"arxiv_id": "quant-ph/0106097",
"authors": [
"M. Ibison",
"B. Haisch"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.54.2737",
"journal_ref": "Phys. Rev. A, vol. 54, pp. 2737-2744 (1996)",
"title": "Quantum and classical statistics of the electromagnetic zero-point field",
"url": "https://arxiv.org/abs/quant-ph/0106097"
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