Abstract:

In this paper, we present a new approach to understanding quantum mechanics using the rotor-router algorithm, also known as the "Propp machine" or "non-random diffusion limited aggregation" algorithm. We demonstrate how this simple algorithm can be used to simulate and observe the effects of interference, such as those seen in the Young double-slit experiment, and how it offers a unique and intriguing perspective on the nature of particles and the fundamental principles of quantum mechanics.

We also introduce the RR phy model, an extension of the rotor-router algorithm, which allows us to explore the role of discrete time and space in the behavior of particles, and to consider the possibility that quantum phenomena may arise from the interactions of particles with their surrounding space.

We present a number of simulations and results, including the effects of adding an absorbing pixel and the emergence of symmetries in the rotor-router algorithm. Overall, we believe that the rotor-router model represents a promising avenue for further exploration and research into the fundamental nature of the universe and its behavior.

Chapters:

1. Introduction

2. The Rotor-Router Algorithm

3. The RR Phy Model

4. Simulating Interference with the Rotor-Router Model

5. Symmetries in the Rotor-Router Algorithm

6. Conclusions and Future Work

Chapter 1: Introduction

In this paper, we present a novel approach to understanding quantum mechanics and the behavior of particles in a given space. This approach is based on the non-random diffusion limited aggregation algorithm, also known as the "Propp machine" or "rotor-router algorithm," which has previously been used to model a variety of phenomena including percolation and aggregation.

We show that the rotor-router algorithm can be extended to simulate the effects of interference, such as those seen in the Young double-slit experiment, and that it can provide insight into the fundamental nature of particles and their interactions with space.

We also introduce the concept of the RR phy model, which expands upon the rotor-router algorithm by incorporating additional physical principles and properties. Through the use of this model, we are able to explore the role of discrete time and space in the behavior of particles, and to consider the possibility that quantum phenomena may arise from the interactions of particles with their surrounding space.

Overall, the rotor-router model and the RR phy model offer a unique and intriguing perspective on the nature of particles and the fundamental principles of quantum mechanics, and provide a promising avenue for further exploration and research into the fundamental nature of the universe and its behavior.