The programme of research underpinning this book had a single objective, which was to explore the viability of the hypothesis that time is discrete rather than continuous. Early on in the writing, it became apparent that there were many theorists from diverse branches of science who have dealt with discrete time mechanics in one form or another. The subject matter of this book therefore is not as esoteric as might be imagined, but can be eminently practical in its applications. Discrete time is also of great interest from a fundamentalist perspective.

One of the most pressing factors driving fundamentalist research is the current state of play concerning the divergences in quantum field theories. Numerous ad hoc fixes have been explored, ranging from the non-integral spacetime dimensions associated with dimensional regularization to lattice gauge theory and string theory. In this respect, discrete time is but one avenue to explore.

Our programme of investigation into discrete time is in no way complete. During the writing of this book, our review of non-standard analysis raised the possibility that the chronon might be best described in terms of infinitesimals. That would then bypass the need to think of an observable scale for any chronon, because infinitesimals have by definition a ‘size’ of zero.

Another feature of our investigation that emerged during the writing of this book is the need to clarify the architecture underpinning any theoretical discussion.