Time of arrival and localization of relativistic particles

Abstract

Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to conflict with the requirement of causality. In this paper, we describe particle localization in terms of time-of-arrival observables, defined in terms of the interaction between a quantum field and a measuring apparatus. The resulting probabilities are linear functionals of QFT correlation functions. Specializing to the case of a scalar field, we identify several timeof-arrival observables differing on the way that the apparatus localizes particle-detection records. Maximum localization is obtained for a unique observable that is related to the Newton-Wigner position operator. Finally, we define a measure of localizability for relativistic particles in terms of a novel time-energy uncertainty relation for the variance of the time of arrival. * anastop@physics.upatras.gr † ksavvidou@upatras.gr

Pointer-based model for state reduction in momentum space

“…Finally, a promising approach towards an operational description of ToF momentum measurements would be the idea of operational time observables defined and investigated for example in Refs. [24][25][26][27][28][29][30]. Instead of using fixed coupling times as in our model, we could replace them by an operational time observable and analyze if this ansatz still leads to meaningful momentum values and a state reduction.…”

“…A similar situation can be found for the time-of-arrival problem [23], which also has a straightforward answer in classical mechanics. However, in the quantum case [24][25][26][27][28][29][30] it becomes a complicated foundational issue, questioning the role of time in the theory [31][32][33][34][35]. In fact one * fabio.di-pumpo@uni-ulm.de needs several operationally defined time-of-arrival operators.…”

Multi-time measurements in Hawking radiation: information at higher-order correlations

“…In recent years, we developed a new method [6][7][8][9] for describing QFT measurements that shares the above property with Glauber's theory. We call this method the Quantum Temporal Probabilities (QTP) method, as its original motivation was to provide a general framework for temporally extended quantum observables [26][27][28].…”

“…The multi-time measurements described here fit naturally with a histories description. The associated probabilities can be defined in terms of history variables and the decoherence functional [6,8,9], i.e., the mathematical object that generalizes the notion of the quantum state and incorporates probabilities in histories theory. Hence, they remain meaningful notions even in non-globally hyperbolic spacetimes, such as the evaporating black hole spacetime of Fig.…”

Open quantum systems and applications to the quantum information theory

“…This means that we must express QFT measurements in terms of Positive-Operator-Valued measures (POVMs). One of us has proposed the use of time-extended observables for the description of particle localization [69]. Time extended observables correspond to POVMs that partly depend upon the dynamics of the quantum system [70].…”