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http://xxx.lanl.gov/list/gr-qc/

gr-qc/0005133 [abs, src, ps, other] :

Title: Vacuum Energy Density Fluctuations in Minkowski and Casimir States via

Smeared Quantum Fields and Point Separation

Authors: Nicholas. G. Phillips, B. L. Hu

Comments: 41 pages, 2 figures

We present calculations of the variance of fluctuations and of the mean of

the energy momentum tensor of a massless scalar field for the Minkowski and

Casimir vacua as a function of an intrinsic scale defined by a smeared field

or by point separation. We point out that contrary to prior claims, the ratio

of variance to mean-squared being of the order unity is not necessarily a

good criterion for measuring the invalidity of semiclassical gravity. For the

Casimir topology we obtain expressions for the variance to mean-squared ratio

as a function of the intrinsic scale (defined by a smeared field) compared to

the extrinsic scale (defined by the separation of the plates, or the

periodicity of space). Our results make it possible to identify the spatial

extent where negative energy density prevails which could be useful for

studying quantum field effects in worm holes and baby universe, and for

examining the design feasibility of real-life `time-machines'.

For the Minkowski vacuum we find that the ratio of the variance to the

mean-squared, calculated from the coincidence limit, is identical to the

value of the Casimir case at the same limit for spatial point separation

while identical to the value of a hot flat space result with a temporal

point-separation. We analyze the origin of divergences in the fluctuations of

the energy density and discuss choices in formulating a procedure for their

removal, thus raising new questions into the uniqueness and even the very

meaning of regularization of the energy momentum tensor for quantum fields in

curved or even flat spacetimes when spacetime is viewed as having an extended

structure. (50kb

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