Can the inertial observer "see" the Unruh accelerated observer's vacuum? The unruh process is asymmetric. The inertial observer is in his vacuum V0 and the accelerated observer measures $\langle V_0|N|V_0 \rangle$ and sees particles. He is not in his vacuum environment.
I wonder if the accelerared observer can act locally on it to get a limited space time region in his vacuum V'?
If he can do that what does the inertial observer "see" in this regieon ? particles ? antiparticles? nothing?
thanks.
Edit: My question is not about the usual unruh effect.
it is not about the accelerated thermometer and why it is like that.
I wonder if the inertial thermometer would still indicate a zero temperature in a given spacetime region in which the accelerated observer would be in his vacuum $V_{acc}$
 A: Let us assume that in uniformly accelerated frame we have a cavity impenetrable to the field (e.g. made from an ideal conductor). Accelerated observer starts removing quanta of thermal Unruh bath from inside the cavity. Walls of the cavity are also needed to be kept refrigerated to below Unruh temperature. The field inside would then be in (Rindler-like) accelerated cavity vaccum state $V_\text{ac}$.
From the Minkowski observer's viewpoint the cavity's inside would contain particles. An inertial detector coupled to the field (e.g. an “atom” initially in its main state) placed inside this cavity could absorb one of these quanta and enter an excited state. But seen from the viewpoint of observer accelerating with the cavity this excitation process would instead be accompanied by an emission of particle.

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*Levin, O., Peleg, Y., & Peres, A. (1992). Quantum detector in an accelerated cavity. Journal of Physics A: Mathematical and General, 25(23), 6471, doi:10.1088/0305-4470/25/23/039.

A modern discussion could be found in a recent paper, this question is  covered in section IIb:

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*Ben-Benjamin, J. S., Scully, M. O., Fulling, S. A., Lee, D. M., Page, D. N., Svidzinsky, A. A., ... & Unruh, W. G. (2019). Unruh acceleration radiation revisited. International Journal of Modern Physics A, 34(28), 1941005, doi:10.1142/S0217751X19410057, arXiv:1906.01729.

