# Hyperbolic metamaterials explained in 5 minutes

How to turn space into time – in the lab

Wouldn’t it be cool if we could turn one dimension of space into an extra dimension of time?  We can’t – but we can fake it!

Einstein showed the only difference between space and time is a minus sign.  So: make a material where light obeys equations with an extra minus sign!

How?  Just take lots of microscopic metal wires and put them in transparent stuff that doesn’t conduct electricity.  Line them all up.  You’ll get something that conducts electricity like a metal in one direction but not the other two directions!

It’s called a hyperbolic metamaterial.  The video explains why.

But why is this like converting a dimension of space into a dimension of time?

Einstein showed that if you have a photon – a particle of light – in a vacuum, it obeys

X² + Y² + Z² – T² = 0

where:

X is the momentum of the light in the x direction
Y is the momentum of the light in the y direction
Z is the momentum of the light in the z direction
T is the momentum of the light in the time direction

(Momentum in the time direction is basically just energy.)

Photons in other stuff obey more complicated equations.  In a hyperbolic metamaterial with wires lined up in the z direction, they obey an equation basically like this:

X² + Y² – Z² – T² = 0

So, the z direction is acting like an extra time dimension! And this lets us do very weird things.

A few warnings if you watch the video:

1) A transparent material like glass is called a dielectric, so you’ll see that word a lot.

2) Instead of writing X, Y, and Z for momentum in the x, y and z direction, physicists often write the letter k with a little x, y, or z under it.

3) Particles are also waves!  The momentum of a particle in some direction is basically just how many times its wave wiggles per meter in that direction.  So, k is also called the wave number.

4) Instead of writing T for the momentum in the time direction, physicists write ω.   This is how much the wave wiggles per second, so it’s also called the frequency

5) When I say ‘basically’, it means I’m leaving out numbers that make things look more complicated, but don’t change the basic idea.