One of the great outstanding challenges in science is to unite general relativity with quantum mechanics, the two great pillars of 20th century science. The problem, of course, is that these theories work on massively different scales.

General relativity describes the large-scale structure of the universe and famously leads to the idea that gravity is intimately linked to the curvature of spacetime. By contrast, quantum mechanics describes the universe at the smallest scale, famously revealing the bizarre and counterintuitive nature of reality at this size.

One way to explore the link between these two theories is to study regions of the universe that are curved on a very small scale. In this way it ought to be possible to study the way that the curvature of spacetime influences quantum fields.

There is a problem, however. The universe only becomes curved on this scale in regions experiencing the most extreme conditions of bending and warping, such as at the beginning of time and at the edges of black holes. Even worse, the mathematics that describes these conditions is so complex that it is almost impossible to solve in anything other than the simplest states.

But all those problems would melt away if it were possible to create curved spacetimes in the lab. Today, Nikodem Szpak at University Duisburg-Essen in Germany has worked out how to do just that.

Szpak’s idea is that ultracold atoms embedded in an optical lattice are mathematically equivalent to a quantum field in a curved spacetime. So instead of solving the equations that describe quantum fields and curved spacetimes, it suddenly becomes possible to measure their behaviour instead in any decent quantum optics lab.

First, some background on optical lattices. When two laser beams overlap they create an interference pattern. By carefully controlling the shape and frequency of the lasers, physicists are able to create interference patterns that take on the shape of egg boxes.

That comes in handy for trapping ultracold atoms, which settle into the minima in the field, just like ping pong balls rolling into an egg box. This structure is called an optical lattice and it is standard fare in any decent quantum optics lab anywhere in the world.

The behaviour of atoms in an optical lattice is interesting. Even when the atoms are close to absolute zero, they do not sit entirely still. That’s because the laws of quantum mechanics allow them to tunnel from one position in the optical lattice to another.

So at any instance, there is finite probability that an atom will hop from one part of the lattice to another. This probability depends on factors such as the strength and shape of the optical field.

Now Szpak has shown why this should be of huge interest to general relativists. Although the movement of the atoms is a discreet, jumping process, it becomes similar to continuous movement when considered on a larger scale, rather in the same way that a series of images viewed quickly appears to show continuous movement.

Szpak has shown that there is a formal mathematical analogy between this movement of atoms through the optical lattice and their movement through a quantum field in a flat spacetime. So the way the atoms move in an optical lattice is equivalent to the way they would move in a quantum field in flat spacetime.

And here’s the thing. When the optical lattice is regular, it is equivalent to a flat space-time. But changing the optical set up so that it varies in space is equivalent to creating a curved space-time.

So in this way, it ought to be a relatively simple matter to simulate the behaviour of a quantum field embedded in curved space-time. “It is striking that atoms hopping in a regularly spaced optical lattice with a trapping potential can behave as if they were moving in a curved space,” says Szpak,

That immediately suggests a number of interesting experiments. For example, by changing the optical field in time, it becomes possible to simulate the expansion or contraction of spacetime as well. That should makes it possible to test the properties of various cosmological expansion models.

And with more complex optical fields, Szpak says it should be possible to simulate the behaviour of relativistic quantum fields in curved spacetimes. “It is also possible to create traveling metric waves, mimicking gravitational waves,” he says.

That is interesting work. These analogue models will not tell physicists anything about the nature of the fundamental physics involved in the most extreme parts of the universe. But they will allow researchers to study the behaviour of known laws under these conditions.

That has not been possible until now because of the tremendous complexity of the mathematics and the difficulty in finding solutions. With these kinds of models, the numerical solutions can be replaced with detailed measurements. “This is the domain where analogue models are expected to facilitate breakthroughs,” says Szpak.

Incidentally, this is not the first time that physicists have described ways of simulating curved spacetime is in the lab. The behaviour of photons inside certain kinds of metamaterials is mathematically equivalent to their behaviour in curved spacetimes and this provides another avenue to study these otherwise extreme conditions.

For the moment, Szpak’s work is entirely theoretical and that raises an obvious question. Since this kind of kit is available in many quantum optics labs around the world, who is going to pick up this ball and run with it? More than a few physicists would be interested to see the results of the first simulations of quantum fields in curved spacetimes.

Ref: arxiv.org/abs/1410.1567 : Curved Spacetimes In The Lab