# Metamaterial Reveals Nature of Time and the Impossibility of Time Machines

By recreating the Big Bang inside a metamaterial for the first time, physicists have shown why the cosmological arrow of time points in the same direction as the thermodynamic arrow of time

Metamaterials are periodic structures that can be engineered to steer light in specific ways. The trick is to manipulate the properties of the “electromagnetic space” in which light travels by controlling the values of the permittivity and permeability of this space.

In recent years, physicists have had a great deal of fun using metamaterials to build all kinds of exciting devices, the best known being invisibility cloaks which steer light around an object, thereby concealing it from view.

But metamaterials have a more profound application because there is a formal analogy between the mathematics of electromagnetic spaces and the mathematics of general relativity and the spacetime it describes.

That means it is possible to reproduce inside a metamaterial an exact copy of many of the features of spacetime. We’ve looked at a number of these ideas, such as how to build a black hole and even create a multiverse.

Today, Igor Smolyaninov at the University of Maryland, College Park, says it is possible to recreate the arrow of time inside a metamaterial. Such an experiment, he says, allows the experimental study of one of the great outstanding mysteries in science: why the cosmological arrow of time is the same as the thermodynamic arrow of time.

At the same time, the exercise gives a curious insight into the potential for time travel.

The arrow of time is a long standing puzzle. Many cosmologists believe that the Universe began with the Big Bang, an event that is clearly in our past.

And yet our standard definition of time comes from thermodynamics and the observation that entropy always increases with time. For example, you can easily break an egg or mix milk into your tea but reversing these processes is hard. Observing phenomena like these defines the arrow of time.

But why should the cosmological and thermodynamic arrows of time point in the same direction?

Metamaterials can help researchers study this problem because it is possible to manipulate them so that space-like dimensions become time-like. Smolyaninov describes how to create a material in which the the x and y directions are space-like while the z-direction is time-like.

The way light moves in this space is exactly analogous to the behaviour of a massive particle in a (2+1) Minkowski spacetime, which is similar to our own universe. So the pattern of light propagation inside this metamaterial is equivalent to the “world lines” of a particle in a Minkowski universe.

Smolyaninov says that a Big Bang event in the metamaterial occurs when the pattern of light rays expands relative to the z-dimension, or in other words, when the world lines expand as a function of time. This establishes a cosmological arrow of time.

The next question is how this arrow relates to a thermodynamic arrow of time. This requires a definition of entropy inside the metamaterial which Smolyaninov says is a kind of measure of the disorder associated with the light rays.

If the metamaterials are perfect the rays should propagate perfectly. But they’re not perfect and so distort the rays as they spread. This determines a thermodynamic arrow of time and shows why it is the same as the cosmological arrow of time.

But there’s a problem of course. Although there is a formal mathematical analogy between these spaces, it’s not at all clear what plays the role in Minkowski space of the imperfect propagation of light through electromagnetic space.

In the past, scientists have only been able to think about these problems theoretically but metamaterials now allow them to s study them experimentally.

Amazingly, Smolynainov and a colleague, Yu-Ju Hung, have actually built their time simulator. Their system is made using specially shaped plastic strips placed on a gold substrate. And the light rays are actually plasmons that propagate across the surface of the metal while being distorted by the plastic strips.

This represents a number of firsts. To start with, Smolyaninov uses this system to recreate the Big Bang in his lab. He calls it a toy Big Bang but it’s hard to understate the significance of this event. A Big Bang in your own lab!

He then goes on to use his model to study the arrows of time. Imagine: your own custom-built arrow of time!

This system also gives an interesting insight into the nature of time machines. The question Smolyaninov asks is whether it is possible to create closed time-like curves in his material. This is equivalent to asking whether it is possible for particles in a Minkowski space to travel in a curve that takes them back to the point in space-time where they started.

He considers this by imagining a cylindrical metamaterial in which the z-dimension and radial dimension are space-like and the angular distance around the cylinder is time-like. Can closed time-like curves exist in this system, he asks. “At first glance, this question is simple, and the answer should be “yes”,” he says.

But under closer examination the answer turns out to be different. He points out that while it is possible for light rays to follow circular paths that return to the point from where they started, these rays would not perceive the angular dimension as time-like.

By comparison, any ray that does perceive the angular dimension as time-like cannot actually return to the same point in space-time, (although it can travel a world line that is very close to a closed time-like curve). So time machines, even trivial ones like this, are impossible.

That’s hugely impressive work. Smolyaninov is one of the world’s leading thinkers on metamaterials and has done much to advance the theory that links electromagnetic and Minkowski spaces.

Now he’s actually getting his hands dirty. In creating for the first time metamaterials that reproduce the Big Bang and the arrows of time that result, he’s surely achieved an extraordinary landmark.

Ref: arxiv.org/abs/1104.0561: Modeling of Time with Metamaterials

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