What is analogue gravity and what is it good for?

Image source: Redbubble. 

Gravity is an exceedingly weak force compared to the other known forces. It dominates at long distances just because, in contrast to the strong and electroweak force, it cannot be neutralized. When not neutralized however the other forces easily outplay gravity. The electrostatic repulsion between two electrons for example is about 40 orders of magnitude larger than their gravitational attraction: Just removing some electrons from the atoms making up your hair is sufficient for the repulsion to overcome the gravitational pull of the whole planet Earth.

That gravity is so weak also means its effects are difficult to measure, and its quantum effects are so difficult to measure that it was believed impossible for many decades. That belief is a troublesome one for scientists because a theory that cannot be tested is not science – in the best case it’s mathematics, in the worst case philosophy. Research on how to experimentally test quantum gravity, by indirect signals not involving the direct production of quanta of the gravitational field, is a recent development. It is interesting to see this area mature, accompanied by the conference series “Experimental Search for Quantum Gravity”.

Alongside the search for observable consequences of quantum gravity – often referred to as the ‘phenomenology’ of quantum gravity – the field of analogue gravity has recently seen a large increase in activity. Analogue gravity deals with the theory and experiment of condensed matter systems that resemble gravitational systems, yet can be realized in the laboratory. These systems are “analogues” for gravity.

If you take away one thing from this post it should be that, despite the name, analogue gravity does not actually mimic Einstein’s General Relativity. What it does mimic is a curved background space-time on which fields can propagate. The background however does not itself obey the equations of General Relativity; it obeys the equation of whatever fluid or material you’ve used. The background is instead set up to be similar to a known solution of Einstein’s field equations (at least that is presently the status).

If the fields propagating in this background are classical fields it’s an analogue to a completely classical gravitational system. If the fields are quantum fields, it’s an analogue to what is known as “semi-classical gravity”, in which gravity remains unquantized. Recall that the Hawking effect falls into the territory of semi-classical gravity and not quantum gravity, and you can see why such analogues are valuable. From the perspective of quantum gravity phenomenology, the latter case of quantized fields is arguably more interesting. It requires that the analogue system can have quantum states propagating on it. It is mostly phonons in Bose-Einstein condensates and in certain materials that have been used in the experiments so far.

The backgrounds that are most interesting are those modelling black hole inflation or the propagation of modes during inflation in the early universe. In both cases, the theory has left physicists with open questions, such as the relevance of very high (transplanckian) modes or the nature of quantum fluctuations in an expanding background. Analogue gravity models allow a different angle of attack to these problems. They are also a testing ground for how some proposed low-energy consequences of a fundamentally quantum space-time might come about and/or affect the quantum fields like deviations from Lorentz-invariance and space-time defects. It should be kept in mind though that global properties of space-time cannot strictly speaking ever be mimicked in the laboratory if space-time in these solutions is infinite. As we discussed recently for example, the event horizon of a black hole is a global property, it is defined as existing forever. This situation can only be approximately reproduced in the laboratory.

Another reason why analogue gravity, though it has been around for decades, is receiving much more attention now is that approaches to quantum gravity have diversified as string theory is slowly falling out of favor. Emergent and induced gravity models are often based on condensed-matter-like approaches  in which space-time is some kind of condensate. The big challenge is to reproduce the required symmetries and dynamics. Studying what is possible with existing materials and fluids in analogue gravity experiments certainly serves as both inspiration and motivation for emergent gravity.

While I am not a fan of emergent gravity approaches, I find the developments in analogue gravity interesting from an entirely different perspective. Consider that mathematics is not in fact a language able to describe all of nature. What would we do if we had reached its limits? We could take out maths as the middle-man and directly study systems that resemble more complicated or less accessible systems. That’s exactly what analogue gravity is all about.

I am sure that this research area will continue to flourish.

(If you really want to know all the details and references, this Living Review is a good starting point.)