dorsal/arxiv
View SchemaImplications of Lorentz covariance for the guidance equation in two-slit quantum interference
| Authors | Peter Holland, Chris Philippidis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302076 |
| URL | https://arxiv.org/abs/quant-ph/0302076 |
| DOI | 10.1103/PhysRevA.67.062105 |
Abstract
It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.
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"abstract": "It is known that Lorentz covariance fixes uniquely the current and the\nassociated guidance law in the trajectory interpretation of quantum mechanics\nfor spin particles. In the non-relativistic domain this implies a guidance law\nfor the electron which differs by an additional spin-dependent term from that\noriginally proposed by de Broglie and Bohm. In this paper we explore some of\nthe implications of the modified guidance law. We bring out a property of\nmutual dependence in the particle coordinates that arises in product states,\nand show that the quantum potential has scalar and vector components which\nimplies the particle is subject to a Lorentz-like force. The conditions for the\nclassical limit and the limit of negligible spin are given, and the empirical\nsufficiency of the model is demonstrated. We then present a series of\ncalculations of the trajectories based on two-dimensional Gaussian wave packets\nwhich illustrate how the additional spin-dependent term plays a significant\nrole in structuring both the individual trajectories and the ensemble. The\nsingle packet corresponds to quantum inertial motion. The distinct features\nencountered when the wavefunction is a product or a superposition are explored,\nand the trajectories that model the two-slit experiment are given. The latter\npaths exhibit several new characteristics compared with the original de\nBroglie-Bohm ones, such as crossing of the axis of symmetry.",
"arxiv_id": "quant-ph/0302076",
"authors": [
"Peter Holland",
"Chris Philippidis"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.67.062105",
"title": "Implications of Lorentz covariance for the guidance equation in two-slit quantum interference",
"url": "https://arxiv.org/abs/quant-ph/0302076"
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