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Two new results concerning the Minkowski vacuum state as seen by Rindler observers are derived. The first result is that the thermal excitations detected by two causally separated Rindler observers are correlated in both energy and phase. Therefore, the state as seen by these observers is similar to an Einstein-Podolsky-Rosen state. The second result suggests that a Rindler observer detects the same thermal spectrum even if there is a boundary condition beyond his horizon. A discussion of what these effects tell us about the origin of the thermal spectrum follows.

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