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Observables in (quantum) General Relativity can be constructed from (quantum) reference frame -- a physical observable is then a relation between a system of interest and the reference frame. A possible interpretation of DSR can be derived from the notion of deformed reference frame (cf Liberati-Sonego-Visser). We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime.

The talk gives a brief overview over different versions of doubly or deformed special relativity (DSR) and its motivation, which comes from the occurrence of a fundamental invariant length in quantum gravity (QG). Despite its QG origin, DSR is a modification of flat space geometry without explicit notion of gravity. In the literature there is a considerable amount of work done to probe deformations of special relativity in classical and quantum mechanics and quantum field theory without taking into account intermediate steps between QG and flat space, like general relativity or quantum field theory in curved space. The more special part of this contribution makes one step into this gap by comparing the DSR modifications of simple quantum scattering of a particle in flat space with the modifications caused by a weak classical gravitational field.

Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are however technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small -- this is the essence of the \'naturalness\' problem. Herein we present an \'emergent\' space-time model, based on the \'analogue gravity\'\' programme, by investigating a specific condensed-matter system that is in principle capable of simulating the salient features of an EFT framework with Lorentz violations. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore our model explicitly avoids the \'naturalness problem\', and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.

The dispersion relations that naturally arise in the known emergent/analogue spacetimes typically violate analogue Lorentz invariance at high energy, but do not do so in completely arbitrary manner. This suggests that a search for arbitrary violations of Lorentz invariance is possibly overkill: There are a number of natural and physically well-motivated restrictions one can put on emergent/analogue dispersion relations, considerably reducing the plausible parameter space.

I will review the shortcomings of the standard account of the origin of anisotropies and in-homogeneities in inflationary cosmology. I will argue that something beyond the established paradigm of physics in needed for a satisfactory explanation of the process by which the seeds of structure emerge from the inflaton vacuum and will consider the application of a generalization of the ideas of R Penrose about a quantum gravity induced dynamical collapse of the quantum mechanical state of a system as a promising avenue to address the issue. I will show i) that the proposal offers paths to test the viability of rather specific ideas about the mechanism of collapse, ii) that generically it can led to some precise features in the primordial spectrum of density fluctuations, which can in turn be looked for, in the observational data, and used to set bounds on certain aspects the quantum gravity phenomenology, and iii) that it leads to other rather robust predictions that can be confronted with experiments.

The possible existence of a physical UV cutoff in dynamical spacetimes raises a number of conceptual and practical questions. If the validity of Lorentz Invariance is considered unreliable above the cutoff, the creation or destruction of quantum modes and the choice of their initial state need to be described explicitly. It has been proposed that these trans-Planckian effects might leave an oscillatory imprint on the power spectrum of inflationary perturbations. However, taking into account the fluctuations of the cutoff, the signal is smeared out beyond recognition.

Quantum fluctuations of spacetime give rise to quantum foam, and black hole physics dictates that the foam is of holographic type. One way to detect quantum foam is to exploit the fact that an electromagnetic wavefront will acquire uncertainties in direction as well as phase as it propagates through spacetime. These uncertainties can show up in interferometric observations of distant quasars as a decreased fringe visibility. The Very Large Telescope interferometer may be on the verge of probing spacetime fluctuations which, we argue, have repercussions for cosmology, requiring the existence of dark energy/matter, critical cosmic energy density, and accelerating cosmic expansion in the present era. We speculate that, in the framework of holographic quantum foam, the dark energy is composed of an enormous number of inert ``particles\'\' of extremely long wavelength. These ``particles\' necessarily obey infinite statistics (quantum Boltzmann statistics) in which all representations of the particle permutation group can occur. For every boson or fermion in the present observable universe there could be ~ 1031 such ``particles\'.

If some form of string theory indeed describes the ultra high energy physics of our universe, then there are two ingredients which are very likely to remain at low energies. The first, is a fifth force in the form of an additional abelian gauge group. The second, and more dramatic, is supersymmetry. Both may be observed at the upcoming Large Hadron Collider. In this talk I will explore a possible intimate connection between these two ingredients which leads to surprising predictions.

Quantum Gravity may be entirely unconventional as a theory, leading to completely unfamiliar (compared to other fields of physics) and unexpected experimental signatures. One particularly interesting avenue for research in that field is the study of models in which quantum gravity operates as a decoherening ``foamy space-time medium\'\', with which ordinary propagating matter interacts. In such theories, which appear to involve the evolution of pure quantum mechanical states to mixed ones, at an effective low-energy level, the CPT operator of the effective low-energy field theory is ill defined, at least in its strong form, as argued in a theorem by R. Wald (1980) . This induces ``Microscopic Time Irreversibility\'\', a fundamental ``arrow of time\'\' in the effective theory. Experimentally of course, this arrow may not be observable: one may face a situation in which the experimentally accessible subspaces of quantum-mechanical states are decoherence-free subspaces, such that the relevant observables appear to be CPT symmetric, despite the strong form of CPT violation. This can happen, for instance, if cancellations of the ``anomalous\'\' CPT Violating terms between particle and antiparticle sectors occur. However, there are concrete quantum-gravity models of space time foam (some within the context of (non-critical) string theory), in which there are clear, and possibly unique (``smoking-gun\'\' type), experimental signatures of such an intrinsic CPT violation, manifesting themselves in induced modifications of the Einstein-Podolsky-Rosen (EPR) correlations of entangled states of neutral mesons in the appropriate meson factories. In the talk I will review the situation in some detail, discussing some indicative estimates of the effect, within some specific (non-critical) string models of space time foam for concreteness, as well as outlining the current experimental limits in phi- and B-meson factories and prospects for improvement in upcoming meson facilities, such as a possible upgrade of DaPhiNe. As I will argue, some models of this type of intrinsic CPT Violation may be falsified in such upgraded facilities.

The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems. I\'ll discuss my recent work in collaboration with Peter Shor which shows that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class.