Abstract
The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated. There is no quantum induced dispersions on the motion of the particle when it is alone in the empty space. However, when a reflecting wall is introduced, dispersions occur with magnitude dependent on how fast the system evolves between the two scenarios. A possible way of implementing this process would be by means of an idealized sudden switching, for which the transition occurs instantaneously. Although the sudden process is a simple and mathematically convenient idealization it brings some divergences to the results, particularly at a time corresponding to a round trip of a light signal between the particle and the wall. It is shown that the use of smooth switching functions, besides regularizing such divergences, enables us to better understand the behavior of the quantum dispersions induced on the motion of the particle. Furthermore, the action of modifying the vacuum state of the system leads to a change in the particle energy that depends on how fast the transition between these states is implemented. Possible implications of these results to the similar case of an electric charge near a perfectly conducting wall are discussed.
Highlights
Reported residual effect at late times, which may be connected to an energy conservation law [7]
The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated
It is shown that the use of smooth switching functions, besides regularizing such divergences, enables us to better understand the behavior of the quantum dispersions induced on the motion of the particle
Summary
This expression assumes a sudden switching regime, as the interaction is sharply limited to the interval 0 < t < τ. We will refer to τ as the measuring time — the interval of time during which the particle is effectively interacting with the field. This description is quite convenient as an idealized model. When only classical aspects are considered, the switching could provide a continuous way connecting the cases when the particle is free of interaction and when it effectively interacts with the field. The sudden process assumed in eq (2.1) is understood as a limiting case for which Fτ (t) → Θ(t)Θ(τ − t), where Θ(t) represents the unit step function, which is equal to 0 for t < 0, and 1 for t ≥ 1
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