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arXiv · 2210.05591

Relativistic time-of-arrival measurements: predictions, post-selection and causality problem

Charis Anastopoulos·Maria-Electra Plakitsi
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Abstract

We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental distinction of different probability assigments is possible especially in near-field measurements. We also analyze causality in relativistic measurements. We consider a quantum state obtained by a spacetime-localized operation on the vacuum, and we show that detection probabilities are typically characterized by small transient non-causal terms. We explain that these terms originate from Feynman-propagation of the initial operation, because the Feynman propagator does not vanish outside the light-cone. We discuss possible ways to restore causality, and we argue that this may not be possible in measurement models that involve switching the field-apparatus coupling on and off.

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Charis Anastopoulos, Maria-Electra Plakitsi. 2022-10-11. Relativistic time-of-arrival measurements: predictions, post-selection and causality problem. https://doi.org/10.3390/foundations3040041

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