# Naturalness in an Emergent Analogue Spacetime

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Matt Visser, Jun 28, 2015 Available from:- [Show abstract] [Hide abstract]

**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 - [Show abstract] [Hide abstract]

**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 pagesJournal of Physics Conference Series 05/2009; DOI:10.1088/1742-6596/189/1/012046 - [Show abstract] [Hide abstract]

**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.