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AIP conference proceedings

Localization of particles, spreading and the notion of Einstein causality

Gerhard C. Hegerfeldt

Published Jan 1, 2001• 1 citation
Publisher

Abstract

The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. We show that under quite general assumptions instantaneous spreading of particle localization occurs in quantum theory, relativistic or not, with fields or without. We discuss if this affects Einstein causality. It is also pointed out that the controversy about recent experiments of Nimtz and coworkers reporting superluminal signal velocities in micro-wave tunneling arise from an indiscriminate use of terminology and that the experimental results are in full agreement with Einstein causality in its ordinary sense.

DOI
10.1063/1.1419340

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The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. We show that under quite general assumptions instantaneous spreading of particle localization occurs in quantum theory, relativistic or not, with fields or without. We discuss if this affects Einstein causality. It is also pointed out that the controversy about recent experiments of Nimtz and coworkers reporting superluminal signal velocities in micro-wave tunneling arise from an indiscriminate use of terminology and that the experimental results are in full agreement with Einstein causality in its ordinary sense.
The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. It is pointed out that Nimtz and coworkers use the notion of signal velocity in a different sense from Einstein and that their experimental results are in full agreement with Einstein causality in its ordinary sense. We also show that under quite general assumptions instantaneous spreading of particle localization occurs in quantum theory, relativistic or not, with fields or without. We discuss if this affects Einstein causality.
The fulfillment in quantum electrodynamics of the principle of relativistic causality—the signal velocity does not exceed the velocity of light—is discussed. In Sec. 1 it is argued that this principle is not guaranteed automatically merely by the local commutativity of the theory. Section 2 is a critical review of the signal transmission problems which have been formulated and solved in the literature. In Sec. 3, this problem is considered in the framework of a simple but fairly realistic model of quantum electrodynamics. The signal source is an external current localized in some region S. The arrival of a signal in a region D at a distance R is established by a change in the coordinate, momentum, or energy of a charged particle. It is shown that proof of relativistic causality of the theory requires one to take into account appropriately quantum-mechanical and, in particular, quantum-electrodynamical features of the problem. In the final fourth section, a general formulation and exact solution of the signal transmission problem are given. The treatment is of sufficient generality for one to be able to assert that in the framework of quantum electrodynamics none of the possible methods of signal transmission violate relativistic causality.
It is shown that the transferring of light signal faster-than-c can take place exclusively as the instantaneous quantum tunneling. Its extent (space size of instanton) must be inversely relative to lack of energy till nearest stable or resonant state. ''Superluminality'' leads to nonlocality ''in small'', in a near field zone, and can be described by 4-vector AμA_μAμ​, the E\mathbf{E}E and H\mathbf{H}H fields remain local. These assertions are proven, independently, in the frameworks of general field theory and by the theory of time duration of scattering, with taking into account the entropy growing. They are correlated with peculiarities of tunneling and frustrated total reflection. The results correspond to the Wigner formulation of causality: ''The scattered wave cannot escape a scatterer before the initial wave reaches it'' and are conformed to experimental data on superluminal transferring.
This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.