Constraining GUP models using limits on SME coefficients

Abstract

Generalized uncertainty principles (GUP) and, independently, Lorentz symmetry violations are two common features in many candidate theories of quantum gravity. Despite that, the overlap between both has received limited attention so far. In this brief paper, we carry out further investigations on this topic. At the nonrelativistic level and in the realm of commutative spacetime coordinates, a large class of both isotropic and anisotropic GUP models is shown to produce signals experimentally indistinguishable from those predicted by the Standard Model Extension (SME), the common framework for studying Lorentz-violating phenomena beyond the Standard Model. This identification is used to constrain GUP models using current limits on SME coefficients. In particular, bounds on isotropic GUP models are improved by a factor of $10^{7}$ compared to current spectroscopic bounds and anisotropic models are constrained for the first time.

On the algebraic approach to GUP in anisotropic space

“…A notable exception is the commutative model derived for f and g i related by the condition (60). This last finding underpins the investigation performed on [27] focused on the physics of such commutative model and should go side by side with it.…”

“…Predictions from other models in Sec. VII might be learned after comparison to the Lorentz-violating Standard Model Extension, in a similar way to what was done in [27,40]. It might also be interesting to investigate whether these models feature minimal length uncertainty and, if so, how the space anisotropy affects it -e.g., the commutator (56) implies a direction-dependent uncertainty of (∆x i ) min ∼ √ β i in the particular case β = diag(β 1 , β 2 , β 3 ), but reaching a definite conclusion in more general situations may be challenging.…”

“…Considering future works, physics from models satisfying the two criteria is largely unexplored and ought to be further investigated. For instance, the approximately commutative model based on (56) is found on [27] to predict annual variations of the 1S-2S hydrogen transition frequency. Predictions from other models in Sec.…”

“…(55) and actually vanishes to O(β) for β ′ = 2β. This particular case was considered in [27] and it was found that searches for annual variations in high precision measurements of the 1S-2S hydrogen transition frequency bounds the trace of β at the 10 −8 GeV −2 level in the laboratory frame. Still for the case β ′ = 2β, the commutator of position and momentum reads…”

“…Back at the nonrelativistic regime, this means that considering GUP in anisotropic space allows accessing a wider range of physical predictions other than those from very specific frames where isotropy holds. Very recently, first steps to consider GUP in this context were reported on [27]. There, motivated by Lorentz symmetry violations as candidate signatures of quantum gravity [28,29], one particular class of GUP models in anisotropic space is proposed and experimentally constrained within the framework of the Standard Model Extension [30][31][32][33] -possible experimental signals in the laboratory frame are placed around the 10 TeV scale [27].…”