Abstract
The isotropy of space is not a logical requirement but rather is an empirical question; indeed there is suggestive evidence that universe might be anisotropic. A plausible source of these anisotropies could be quantum gravity corrections. If these corrections happen to be between the electroweak scale and the Planck scale, then these anisotropies can have measurable consequences at short distances and their effects can be measured using ultra sensitive condensed matter systems. We investigate how such anisotropic quantum gravity corrections modify low energy physics through an anisotropic deformation of the Heisenberg algebra. We discuss how such anisotropies might be observed using a scanning tunnelling microscope.
Highlights
The isotropy of space is not a logical requirement but rather is an empirical question; there is suggestive evidence that universe might be anisotropic
Any theory of quantum gravity, upon integrating out some degrees of freedom to obtain a low energy effective action, must yield general relativity. This implies that local Lorentz symmetry might break due to quantum gravitational effects[1,2], and emerge only as a low energy effective symmetry that is not expected to hold at sufficiently high energies
A similar phenomenon has been observed in condensed matter physics, where isotropy emerges in graphene when only the nearest-neighbour atom contributions are considered, whose physics can be expressed via a (2 + 1) dimensional Dirac e quation[13,14]
Summary
It is conceivable that observed anisotropies in the Cosmic Microwave Background (CMB)[27,28] could be explained by quantum gravitational e ffects[29,30] and could be produced during inflation[31,32,33,34] Such effects would modify field theories from their continuum limit formulations, and their leading order corrections could be expressed by an anisotropic GUP-like deformation. The aim in this paper is to analyze the implications of an anisotropic GUP and sketch out some possible pathways to experimentally test the presence of spacetime anisotropy at short distances As this can again be done using non-relativistic ultra sensitive condensed matter systems, we can neglect the effects of Lorentz symmetry for the anisotropic GUP.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
