What is (3-1) dimension? Can other dimensions be ‘created’ as well?

This is quite a complicated question, but I will do my best to explain it to you as simply as possible.

The fact is that Albert Einstein in his generalized theory of gravity (general relativity) linked the concepts of space and time in an inextricable way. He combined these fundamental concepts in the new concept of “a spacetime”. This is an abstract mathematical model that captures the background on which the events of our universe play out. An important concept here is the measure of the distance between two points (events) in spacetime. The so-called metric (dS²). In a flat space, in the absence of large masses or energy, it is given in good approximation by:

dS²=-c²dt²+dx²+dy²+dz².

You notice that a time interval (dt) makes a negative contribution to the metric and the spatial intervals (dx, dy and dz) a positive one. This is a fundamental difference between the spatial coordinates and the time coordinate. The metric described above has 3 spatial coordinates and 1 time coordinate and is therefore referred to as a spacetime with a (3,1) signature. In the presence of large masses, according to general relativity, spacetime will be curved and the metric will be adjusted.

The remainder of your question deals with metamaterials and the so-called transformation optics. After all, a few years ago it was discovered that the propagation of light through such an arbitrary metric is completely equivalent to the propagation of light through materials with exotic optical properties. These materials do not occur in nature and are made by scientists at the nanoscale. These are called metamaterials. Indeed, three-dimensional metamaterials have recently been created that mimic a metric with a (2,1) signature. In other words, a material of which 1 direction is perceived by light as a time coordinate and the other two directions as spatial coordinates.

This technique (transformation optics) in which properties of the universe are imitated in a metamaterial has consequences for both fundamental and applied physics. At a fundamental level, it enables us to observe the difficult-to-control interaction of light with black holes in a laboratory. For applied physics, transformation optics provides a recipe for designing optical components that display special functionalities based on effects we observe in the universe.

I hope this answered your question as best as possible.

kind regards,

Vincent