Causal evolution of wave packets

Eckstein, Michał; Miller, Tomasz

doi:10.1103/physreva.95.032106

Cited by 22 publications

(33 citation statements)

References 61 publications

(131 reference statements)

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“…The first application of the presented theory to the study of causality in quantum theory is discussed in details in [21]. Therein, we focus on the wave packet formalism, which is in common use in atomic, condensed matter [53] and particle physics [12], as an approximation to complicated QFT problems.…”

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confidence: 99%

Causality for Nonlocal Phenomena

Eckstein

Miller

2017

Ann. Henri Poincaré

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Abstract.Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between Lorentzian geometry, topology and measure theory. We provide various characterisations of the proposed causal relation, which turn out to be equivalent if the underlying spacetime has a sufficiently robust causal structure. We also present the notion of the 'Lorentz-Wasserstein distance' and study its basic properties. Finally, we outline the possible applications of the developed formalism in both classical and quantum physics.

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confidence: 99%

Causality for Nonlocal Phenomena

Eckstein

Miller

2017

Ann. Henri Poincaré

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“…Furthermore, the quantum measurement effectuates a dramatic change on particle's dynamics. In consequence, although several formal results [13][14][15][16][17][18] suggested that quantum wave packets can propagate superluminally, it was unclear whether it implies operational faster-than-light communication (cf. for instance [16] vs [19] or a more recent work [20]).…”

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confidence: 99%

Operational causality in spacetime

et al. 2020

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The no-signalling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation -the 'dynamical no-signalling principle' -, which forbids superluminal signalling via measurements on simple physical objects (e.g. particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal -it can be applied to any theory (classical, quantum or post-quantum) with well-defined rules of calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schrödinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or post-quantum dynamics.

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“…Subsequently, we briefly sketch the rudiments of noncommutative geometry à la Connes [4]. Next, we discuss the notion of causality suitable in this context, summarising the outcome of our recent works [18][19][20][21][22][23][24][25][26]. Finally, we explain how the presumed noncommutative structure of spacetime extorts a modification of the axioms of quantum field theory and thus might yield empirical consequences.…”

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confidence: 99%