(a) Randomly generated instantaneous microscopic fractal map of dielectric permittivity in a mixture of aniline and cyclohexane just below the critical temperature Tc. (b) Same map as it looks if probed with small kz photons. (c) A similar fluctuating permittivity distribution, as it would be perceived by extraordinary photons propagating in a layered hyperbolic metamaterial at ω just below ω0. Areas shown in red appear as “virtual black holes”.
Arxiv – Virtual Black Holes in Hyperbolic Metamaterials (11 pages) Metamaterials should allow scientists recreate and study the properties of space time on the smallest scale.
Optical space in electromagnetic metamaterials may be engineered to emulate various exotic space-time geometries. However, these metamaterial models are limited in many respects. It is believed that real physical space-time strongly fluctuates on the Planck scale. These fluctuations are usually described as virtual black holes. Static metamaterial models introduced so far do not exhibit similar behavior. Here we demonstrate that thermal fluctuations of optical space in hyperbolic metamaterials lead to creation of virtual electromagnetic black holes. This effect is very large if the dielectric component of the metamaterial exhibits critical opalescence.
We’ve already talked about the first black hole made using a metamaterial and seen how it ought to be possible to recreate (simulations of the physics) of the Big Bang and even entire multiverses.
Now we have another exotic idea. One of the leading thinkers in this area is Igor Smolyaninov at the University of Maryland in College Park. Today, he shows how to create quantum foam inside a metamaterial.
First, a quick backgrounder about quantum foam. Nobody is quite sure what laws of physics govern spacetime on the smallest scale, that’s over the Planck length of about 10^-35 metres. However, our best guess is that quantum mechanics must somehow prevail. And if that’s the case then Heisenberg’s uncertainty principle must play an important role.
This principle implies that to discover anything about a region of space on that scale, we would have to use energies so high that they would create a black hole. (That’s why it doesn’t make sense to think of anything smaller.)
Now, because these black holes can exist, quantum mechanics suggests that they do exist, constantly leaping in and out of existence at the Planck scale.
These “virtual black holes” give spacetime a certain strange structure at the Planck scale. For want of a better word, physicists call it quantum foam.
So what’s this got to do with metamaterials? Smolyaninov points out that metamaterials are only transparent for photons of a specific wavelength when their dielectric permittivity is engineered to be below some critical value.
Should it rise above this value, the material would suddenly become opaque.
So his idea is to create a metamaterial in which the dielectric permittivity is just blow this critical value. Then any thermal fluctuations inside the material ought to raise the permittivity, making the material opaque in that region.
So any photons caught in that region will be trapped. “They experience total internal reflection at any incidence angle,” says Smolyaninov.
That region is therefore an analogue of a black hole. And the fact that these black holes will spring in and out of existence as the temperature naturally fluctuates means that the metamaterial behaves like quantum foam.
But the best thing is that this quantum foam effect ought to be straightforward to see. Smolyaninov says there are well known systems that sit at this critical juncture between transparency and opacity. He points in particular to a mixture of aniline and cyclohexane which is immiscible below 35 degrees C. Above this temperature, however, the liquids happily mix, creating regions with differing permittivity.
The interesting effect occurs in the layer between them as they mix, which becomes entirely opaque at the critical temperature. But because of thermal fluctuations, small regions are constantly flickering in and out of opacity, trapping and releasing light in the process. “This behaviour is rather similar to the behaviour of actual physical spacetime on the Planck scale,” says Smolyaninov.
In other words, at the critical temperature this stuff is analogous to quantum foam.
Smolyninov hasn’t actually done this experiment but there’s nothing about it that seems particularly tricky. You could do it in an ordinary flask or test tube. In fact, he ends his paper saying: “This effect appears to be large and easy to observe.”
Which means that sometime soon, physicists will have their own version of quantum foam to play with in the lab.
We have considered hyperbolic metamaterials made using dielectrics exhibiting critical opalescence, and demonstrated that effective “optical space” in such materials may experience strong fluctuations. Similar to the space-time behaviour on the Planck scale, these fluctuations give rise to virtual electromagnetic black holes. Thus, using hyperbolic metamaterials we may emulate such an interesting feature of the real physical space-time as virtual microscopic black holes. This effect appears to be large and easy to observe.
Schematic views of the (a) “wired” and (b) “layered” nonlinear hyperbolic metamaterials made of either metal wires or metal layers inside a dielectric Kerr medium. (c) Hyperbolic dispersion relation allowing unbounded values of the wavevector (blue arrow).