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We propose a scheme to study the effect of motion on measurements of a quantum field carried out by a finite-size detector.
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Consider the state of a single particle accessible to the detector, d ^ † | 0 ⟩ \hat{d}^{\dagger}|0\rangle . The position-space representation of this single particle state, is ⟨ 0 | ϕ ^ d † | 0 ⟩ = ψ D \langle 0|\hat{\phi}d^{\dagger}|0\rangle=\psi_{\text{D}} . It is well-known, however, that a relativistic particle can not be localised any smaller than its characteristic wavelength without superimposing negative frequencies in its wave-packet (i.e., a massive particle can not be localised any smaller than its Compton wavelength). However, in the massless case, the characteristic frequency of the mode is arbitrary and can be specified at will. Therefore, in principle any desired degree of localisation can be achieved by choosing a sufficiently large characteristic frequency for the transmitted mode. We don’t take the limit of infinitesimally small wavepackets, focusing only on physically realisable cases. One should not confuse the word localised
Cited in the paper.
T. G. Downes, T. C. Ralph, and N. Walk, arXiv:1203.2716
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T. D. Downes, I. Fuentes, and T. Ralph, Phys. Rev. Lett. 106
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