Limits to causality and delocalization in classical field theory (Q2708582)

In a paper by \textit{G. C. Hegerfeldt} [Phys. Rev. Lett. 72, 596-599 (1994)] it was shown how the positivity of the Hamiltonian leads to delocalization and superluminal effects in both, relativistic and non-relativistic, quantum theory. In this paper, the authors study these effects in the context of classical field theories. More precisely, the case of a scalar field interacting with a harmonic oscillator is considered. Then, given a wave packet approaching a harmonic oscillator at rest at the origin of coordinates, it is shown that the oscillator is excited before the wave packet touches it, violating Einstein's causality. Although the model does not include violation of relativity since the particle is described by a classical non-relativistic equation, the authors believe that in a complete relativistic model many of their conclusions should remain valid. The main conclusion is, then, that localization leads to difficulties even in classical field theory, excluding the possibility that the effect in quantum theory is due to zero point fluctuations. The authors also mention that they have calculated deviations from causality in the interaction model between dressed particles and the field, for quantum mechanical systems. Since nobody has yet observed such deviations from causality, the authors comment the two possibilities obtained as a consequence of their results: other Einstein's causality is only an approximation, or there is something wrong in the usual approach to field theory.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00037].