A COMMENT ON ENTROPY AND AREA

For an arbitrary quantum field in flat space with a planar boundary, a n entropy of entanglement, associated with correlations across the bou ndary, is present when the field is in its vacuum state. The vacuum st ate of the same quantum field appears thermal in Rindler space, with a n associated thermal entropy. We show that the density matrices descri bing the two situations are identical, and therefore that the two entr opies are equal. We comment on the generality and significance of this result, and make use of it in analyzing the area and cutoff dependenc e of the entropy. The equivalence of the density matrices leads us to speculate that a planar boundary in Minkowski space has a classical en tropy given by the Bekenstein-Hawking formula.