Abstract
In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.
Highlights
Since the establishment of quantum mechanics and general relativity, there has been a constantly growing effort to merge quantum and gravitational effects at arbitrary energy scales in a complete and consistent theoretical framework
In a quantum mechanical setting, such a feature can be incorporated by extending the Heisenberg uncertainty principle (HUP) with the addition of a position-dependent correction that introduces a non-vanishing minimal uncertainty in momentum [11,12,13,14,15] and provides a form of an extended uncertainty principle (EUP)
In order to quantify the breakdown of Lorentz symmetry induced by the EUP, we consider a string-theoretical effective field theory according to which any operator appearing in the Standard Model (SM) Lagrangian is contracted with Lorentz-violating fields [39,40]
Summary
Since the establishment of quantum mechanics and general relativity, there has been a constantly growing effort to merge quantum and gravitational effects at arbitrary energy scales in a complete and consistent theoretical framework. In order to quantify the breakdown of Lorentz symmetry induced by the EUP, we consider a string-theoretical effective field theory according to which any operator appearing in the Standard Model (SM) Lagrangian is contracted with Lorentz-violating fields [39,40] This model is known as the Standard Model Extension (SME), and we will focus in particular on its gravity sector [41,42] in the non-relativistic limit [43].
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