Naturalness in an Emergent Analogue Spacetime

International School for Advanced Studies and INFN, Via Beirut 2-4, 34014 Trieste, Italy.
Physical Review Letters (Impact Factor: 7.51). 05/2006; 96(15):151301. DOI: 10.1103/PhysRevLett.96.151301
Source: arXiv


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" spacetime model, based on the "analogue gravity" program, by investigating a specific condensed-matter system. 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.

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    • "The key idea behind Hořava–Lifshitz gravity is to sacrifice local Lorentz symmetry in exchange for renormalizability: Local Lorentz symmetry is violated at the non-perturbative level of our field theory, but will hopefully be recovered at long distance / low energy scales. The particular kind of Lorentz violations we will encounter here have been discussed to some extent within quantum gravity phenomenology [5] [6] [7]. Let us consider the following class of theories that break Lorentz invariance fundamentally, and that at the kinematical level lead to a dispersion relation which is some function of momentum and mass, E 2 = m 2 + p 2 → E 2 = F (p, m). "
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    ABSTRACT: Approximately one year ago Hořava proposed a power-counting renormalizable theory of gravity which abandons local Lorentz invariance. The proposal has been received with growing interest and resulted in various different versions of Hořava-Lifshitz gravity theories, involving a colourful potpourri of new terminology. In this proceedings contribution we first motivate and briefly overview the various different approaches, clarifying their differences and similarities. We then focus on a model referred to as projectable Hořava–Lifshitz gravity and summarize the key results regarding its viability.
    Journal of Physics Conference Series 05/2010; 222(1):012054. DOI:10.1088/1742-6596/222/1/012054
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    • "It has been well established, see [11] [12] [13] [14] [15], that small perturbations around the condensate experience an effective / acoustic / emergent spacetime geometry. In this context Lorentz symmetry is not an exact symmetry, it is emergent [16] [17] [18] [19] [20] [21]. Previously, see [17] [22], we have shown that the signature of the emergent spacetime geometry is related to the nature of the interaction between the fundamental bosons, and that it is possible to drive (sudden) finite transitions between periods of different spacetime signature. "
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    ABSTRACT: We investigate the behaviour of quantum fields coupled to a spacetime geometry exhibiting finite regions of Euclidean (Riemannian) signature. Although from a gravity perspective this situation might seem somewhat far fetched, we will demonstrate its direct physical relevance for an explicitly realizable condensed matter system whose linearized perturbations experience an effective emergent spacetime geometry with externally controllable signature. This effective geometry is intrinsically quantum in origin, and its signature is determined by the details of the microscopic structure. At the level of the effective field theory arising from our condensed matter system we encounter explicit anisotropic scaling in time and space. Here Lorentz symmetry is an emergent symmetry in the infrared. This anisotropic scaling of time and space cures some of the technical problems that arise when working within a canonical quantisation scheme obeying strict Lorentz invariance at all scales, and so is helpful in permitting signature change events to take place. Comment: Based on a presentation by Silke Weinfurtner at the NEB XIII conference in Thessaloniki in June 2008; 9 pages
    Journal of Physics Conference Series 05/2009; 189. DOI:10.1088/1742-6596/189/1/012046
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    • "We already have at least one very concrete and specific example of such a behaviour in the " acoustic spacetimes " that emerge upon linearizing the equations of (non-relativistic, irrotational, barotropic, inviscid) fluid dynamics [3] [4] [5] [6], and there are a large number of more general situations in which " analogue spacetimes " can be constructed [7] [8] [9] [10] [11] [12] [13]. Once one attempts to generalize the acoustic spacetimes to nontrivial dispersion relations, where the phase and group velocities can differ and have nontrivial energy and momentum dependence [10] [11] [12] [13], then one is very naturally lead to one specific class of incarnations of the notion of " rainbow geometry " [1]. Furthermore under a plausible set of working hypotheses this class of " rainbow geometries " is remarkably similar to the class naturally arising from " quantum gravity phenomenology " [1]. "
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    ABSTRACT: There is a possibility that spacetime itself is ultimately an emergent phenomenon, a near-universal "low-energy long-distance approximation", similar to the way in which fluid mechanics is the near-universal low-energy long-distance approximation to quantum molecular dynamics. If so, then direct attempts to quantize spacetime are misguided - at least as far as fundamental physics is concerned. Based on this and other considerations, there has recently been a surge of interest in the notion of energy-dependent and momentum-dependent "rainbow'' geometries. In the present article I will not discuss these exotic ideas in any detail, instead I will present two specific and concrete examples of situations where an energy-dependent "rainbow'' geometry makes perfectly good mathematical and physical sense. These simple examples will then serve as templates suggesting ways of proceeding in situations where the underlying physics may be more complex. The specific models I will deal with are (1) acoustic spacetimes in the presence of nontrivial dispersion, and (2) a mathematical reinterpretation of Newton's second law for a non-relativistic conservative force, which is well-known to be equivalent to the differential geometry of an energy-dependent conformally flat three-manifold. These two models make it clear that there is nothing wrong with the concept of an energy-dependent "rainbow'' geometry per se. Whatever problems may arise in the implementation of any specific quantum-gravity-inspired proposal for an energy-dependent spacetime are related to deeper questions regarding the compatibility of that specific proposal with experimental reality.
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