Metamaterial model of fractal time

TL;DR

This paper introduces a metamaterial system that models a fractal time dimension within an effective 2+1 Minkowski spacetime, challenging the traditional view of smooth, one-dimensional time.

Contribution

It presents a physical metamaterial model where the time-like variable exhibits fractal properties, specifically with a fractal dimension of D=2, providing a new way to study fractal time.

Findings

The system effectively models a fractal time dimension.

Time-like variable in the system has fractal dimension D=2.

Demonstrates a physical realization of fractal time in metamaterials.

Abstract

While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by effective three-dimensional (2+1) Minkowski spacetime. The peculiar feature of this system is that its time-like variable has fractal character. The fractal dimension of the time-like variable appears to be D=2.