Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?

Yen Chin Ong

doi:10.1140/epjc/s10052-020-8363-2

Abstract

The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the “extended uncertainty principle” (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de Sitter case). We compare the results with previous works in the EUP literature, which are not all consistent. Our result further highlights an important issue in the literature of generalizations of the uncertainty principle: how much can heuristic derivations be trusted?

Highlights

Consider a virtual electron-positron pair in a constant electric field of strength1 E
2 Schwinger pair production in anti-de sitter spacetime The Schwinger pair production rate receives a correction in the presence of a nonzero cosmological constant
extended uncertainty principle” (EUP) was motivated by Park from the point of view that such a form of the uncertainty principle would allow a heuristic derivation of the Hawking temperature of black holes in anti-de Sitter (AdS) or dS spacetimes [11]

Summary

Schwinger pair production from the uncertainty principle

The quantum vacuum is teeming with virtual particles, whose fleeting existence is governed by the uncertainty principle. If we apply a sufficiently strong external electric field, we can “boil the vacuum” [1] and create real particle pairs from the virtual ones This is the well known Schwinger effect [2]. The vast literature of generalizations of uncertainty principles to curved spacetimes and/or considering quantum gravitational effects, is full of various heuristic arguments, and the results are not all consistent with one another. We will discuss this discrepancies in details in this work. This raises the important issue that is not resolved in this work: how much can heuristic derivations be trusted?

Schwinger pair production in anti-de sitter spacetime

The sign of extended uncertainty principle parameter

Discussion: can heuristic arguments be trusted?