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

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?

Dymnikova-Schwinger traversable wormholes

“…The gravitational counterpart of this a phenomenon holds some similarity with that one associated to the Casimir effect, which has been widely studied in the context of wormholes [16][17][18][19][20]. Thus, on considering the correction to the Schwinger effect due to the introduction of a minimal length ( = √ α) via GUP [31,32], we have found the corresponding correction to the gravitational analogue of Dymnikova's matter distribution. Supposing that the minimal length is very small, we obtained a novel traversable and asymptotically flat wormhole solution that reduces to the one previously studied when α = 0 and d = 4, for the same redshift function employed before.…”

“…The correction to the Schwinger effect associated to the existence of a minimal length was obtained in [31,32] by means of the Generalized Uncertainty Principle (GUP). In this case, the electron-positron pair production rate becomes…”

“…The shape function of Dymnikova-Schwinger GUP-corrected wormhole can be obtained from the (t, t) component of Einstein's equations, (13), for d = 4, with the energy density profile (32), and it can be written as…”

“…We will study their principal properties, such as embedding diagrams, Weak and Null Energy Conditions (WEC and NEC), and the position-dependent state parameter. Following, we will specialize this analysis for a 4-dimensional universe and, by formally associating the Dyminikova density profile with the Schwinger particle-antiparticle pair production in a vacuum according to [29,30], we will correct the model introducing a fundamental minimal length via Generalized Uncertainty Principle (GUP) following [31,32]. With this, we find a novel traversable and asymptotically flat wormhole solution and also study those properties, remarking on the role of the minimal length in them.…”

A Critique on Some Aspects of GUP Effective Metric

“…It is true that different QG theories and/or models lead to different type of GUPs, but even for a given GUP, like the simplest one discussed in this work, it is far from obvious how to obtain an effective metric. We certainly cannot simply rely on heuristic arguments and our intuitions [30]. Of course the concept of a metric -that of a well-defined smooth Lorentzian geometry -is probably not so useful in the full QG regime where GUP effects become important.…”