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Phys. Rev. D 66, 124012 (2002) [7 pages]

Spatially averaged quantum inequalities do not exist in four-dimensional spacetime

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L. H. Ford*
Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155

Adam D. Helfer†
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Thomas A. Roman‡
Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155

Received 20 August 2002; published 26 December 2002

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multimode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.

© 2002 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.66.124012
DOI:
10.1103/PhysRevD.66.124012
PACS:
04.62.+v, 03.70.+k, 42.50.Dv

*Email address: ford@cosmos.phy.tufts.edu

†Email address: adam@math.missouri.edu

‡Permanent address: Department of Physics and Earth Sciences, Central Connecticut State University, New Britain, CT 06050. Email address: roman@ccsu.edu

 
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