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Problems with the Newton–Schrödinger equations

dc.contributor.authorAnastopoulos, C
dc.contributor.authorHu, B.L.
dc.identifier.citationC Anastopoulos and B L Hu 2014 New J. Phys. 16 085007 doi:10.1088/1367-2630/16/8/085007en_US
dc.descriptionFunding for Open Access provided by the UMD Libraries Open Access Publishing Fund.
dc.description.abstractWe examine the origin of the Newton–Schrödinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the ‘Moller–Rosenfeld equation’) based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of N particles as N → ∞, not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the nonrelativistic limit of quantum electrodynamics. They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR +QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the ‘collapse of the wave function’, we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.en_US
dc.publisherIOP Publishingen_US
dc.subjectgravitational decoherenceen_US
dc.subjectNewton-Schrödinger equationen_US
dc.subjectgravitational quantum physicsen_US
dc.subjectsemiclassical gravityen_US
dc.subjectnonlinear Schrödingeren_US
dc.titleProblems with the Newton–Schrödinger equationsen_US
dc.relation.isAvailableAtCollege of Computer, Mathematical & Natural Sciencesen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, MD)en_us

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