This thesis deals primarily with the phenomenology associated to quantumudaspects of spacetime. In particular, it aims at exploring the phenomenologicaludconsequences of a fundamental discreteness of the spacetime fabric,udas predicted by several quantum gravity models and strongly hinted byudmany theoretical insights.udThe first part of this work considers a toy-model of emergent spacetimeudin the context of analogue gravity. The way in which a relativistic Bose–udEinstein condensate can mimic, under specific configurations, the dynamicsudof a scalar theory of gravity will be investigated. This constitutes proof-ofconceptudthat a legitimate dynamical Lorentzian spacetime may emerge fromudnon-gravitational (discrete) degrees of freedom. Remarkably, this modeludwill emphasize the fact that in general, even when arising from a relativisticudsystem, any emergent spacetime is prone to show deviations from exactudLorentz invariance. This will lead us to consider Lorentz Invariance Violationsudas first candidate for a discrete spacetime phenomenology.udHaving reviewed the current constraints on Lorentz Violations and studiedudin depth viable resolutions of their apparent naturalness problem, theudsecond part of this thesis focusses on models based on Lorentz invariance.udIn the context of Casual Set theory, the coexistence of Lorentz invarianceudand discreteness leads to an inherently nonlocal scalar field theory overudcausal sets well approximating a continuum spacetime. The quantum aspectsudof the theory in flat spacetime will be studied and the consequencesudof its non-locality will be spelled out. Noticeably, these studies will lendudsupport to a possible dimensional reduction at small scales and, in a classicaludsetting, show that the scalar field is characterized by a universal nonminimaludcoupling when considered in curved spacetimes.udFinally, the phenomenological possibilities for detecting this non-localityudwill be investigated. First, by considering the related spontaneous emissionudof particle detectors, then by developing a phenomenological model to testudnonlocal effects using opto-mechanical, non-relativistic systems. In bothudcases, one could be able to cast in the near future stringent bounds on theudnon-locality scale.
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