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.
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