Signalled Diffusion Book I - Foundations

I'm bringing out a series of short books on the subject signalled diffusion.The first book can be found here. Below I have reproduced the introduction.  I hope that this introduction will explain why I call it Signalled Diffusion and where I hope this project is taking me. 

Introduction

The one-dimensional elementary diffusion equation can be written as:

1.0

…where Y is the “diffusing” quantity, a quantity which is a function of time t and spatial coordinate x and where D is the diffusion constant.

In terms of modelling real situations this equation can be used to represent a statistical description for the transport of particulate matter, where chaotic interactions ensure that each particle of matter is, to all intents and purposes, subject to random walk. If we are dealing with large numbers of randomly walking particles then Y is a statistical quantity which gives a measure of the density of matter at a point in space and time. However, if we are talking about a small number of randomly walking particles Y breaks down as a density value and must then be used as a measure of the probability of finding a particle at a particular point in space and time. In this latter case Y is no longer a literal physical variable since for lone particles it corresponds to no measurable quantity; rather it encapsulates the level of information we as observers have about a particle’s movements. When interpreted as a probability Y is not just about the ontology of the world beyond, but also about the observer and his relation to the world via the information he holds about it.

When used as a probability envelope Y is a cognitive projection onto reality: For if a particle moves around according to random walk there is no literal curve Y to be observed out there; rather it is more akin to a shadowy background influence which has the potential to be used to predict statistical outcomes of a large aggregate of particles. Therefore if Y is a probability it is less a direct ontological reality than it is an epistemic device facilitating the calculation of statistics.

In this series of books, however, I will be exploring what happens if we treat the envelopes in Y as ontologically real and particles as the cognitive projection. To this end I envisage diffusion not as the statistical outcome of the literal stepping of randomly walking particles but rather a result of signals being sent between the points in space and those points accumulating the values received in such a way as to give us a quantity Y which replicates the diffusion equation. I believe that by using this approach it becomes possible to make sense of quantum mechanics as a form of signalled random walk. How this works out in practice I hope will become clearer as I proceed.

This series of books explores the foundations of signalled diffusion and supplements my book Gravity and Quantum Non-Linearity and its more concise version Gravity from Quantum Non-linearity. In both works the emphasis was to arrive at an explanation of gravity. In this series of short books, however, I hope to explore the fundamentals of the subject more thoroughly and remedy some of the faults and short falls in my first book. But whether any of this is going to lead me onto anything significant as the series develops remains to be seen.