Rindler observers, correlated states, boundary conditions, and the meaning of the thermal spectrum

Abstract

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.

Unruh effect without trans-horizon entanglement

“…The transition rates of a particle detector in the presence of a plane boundary have been discussed by several authors [15][16][17]. To our knowledge, however, none of them has drawn what we consider the salient conclusion of this calculation: it shows that the Unruh effect is not just about entanglement with hidden degrees of freedom.…”

Teleportation with a Uniformly Accelerated Partner

“…It is well appreciated now [8,9,10,11,12,13] that the quantization of fields in Minkowski and Rindler coordinates are inequivalent, implying that the RRW vacuum seen by Rob |0 I is different than the Minkowski vacuum seen by Alice |0 M . The celebrated result of Davies and Unruh [9] is that the Minkowski vacuum can be written in terms of the region I and II states (for a scalar field) as…”

Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method

“…It was concluded that the Unruh effect remains a low energy phenomenon as the correction to thermality is inversely proportional to the square of the cutoff scale in the modified dispersion relation. Now, it turns out that the approach based on the Unruh-DeWitt point-like detector can also be viewed as a relativistic Doppler shift calculation [37,[59][60][61][62]. Although such a point of view is extremely intuitive, it has not been much mentioned in the literature regarding the Unruh effect, and never discussed regarding the case of modified dispersion relations.…”