Combinatorial Physics

The following sections are included:

• Preface

• Contents

The book is an essay in the foundations of physics; it presents a combinatorial approach; ideas of process fit with a combinatorial approach; quantum physics is naturally combinatorial and high energy physics is evidently concerned with process. Definition of 'combinatorial'; the history of the concept takes us back to the bifurcation in thinking at the time of Newton and Leibniz; combinatorial models and computing methods closely related.

Theory-language defined to make explicit the dependence of modern physics on Newtonian concepts, and to make it possible to discuss limits to their validity; Leibniz' relational, as opposed to absolute, space discussed; the combinatorial aspect of the monads.

Bohr's attempt to save the quantum theory by deducing the wave-particle duality, and thence the formal structure of the theory, from a more general principle (complementarity) examined: the view of complementarity as a philosophical gloss on a theory which stands up in its own right shown to misrepresent Bohr: Bohr's argument rejected — leaving the quantum theory still incomprehensible.

Physics not scale-invariant; it depends on some numbers which come from somewhere outside to provide absolute scales; the classical kind of measurement cannot in the nature of the case provide them; measurement is counting; the coupling constants are the prima-facie candidates; this was Eddington's conjecture; the question is not whether we find combinatorial values for these constants, but how we do so; current physics puts the values in ad hoc.

The combinatorial model used is hierarchical; the algorithm relating the levels is due to Parker–Rhodes; the construction is presented in several ways each stressing a particular connection with physics: (1) similarity of position, (2) the original combinatorial hierarchy, (3) counter firing, (4) limited recall, (5) self-organization, (6) program universe.

The elementary process expressed algebraically and interpreted as decision whether to incorporate a presented element as new; new elements labelled; the need for labelling to be consistent gives central importance to discriminately closed subsets; any function which can assign labels equivalent to one which represents process; process defined as always using the smallest possible extension at each step that is allowed by the previous labelling; representation of functions by arrays; representation of arrays by matrices and strings familiar from the simpler treatments of Chapter 5; summary of the argument.

The primary contact with experiment in quantum physics comes through counting in scattering processes; coupling constants are ratios of counts which specify the basic interactions; this outline picture has to be modified to get the experimental values; history of attempts to calculate the fine-structure constant reviewed; explanations of and calculations of the non-integral part due to McGoveran and to Kilmister given. The latter follows better from the principles of construction of the hierarchy algebra of Chapter 6.

Comments provided on high energy physics and the particle/quantum number concept from the standpoint regarding the basic interactions of Chapter 7; the particle is the conceptual carrier of a set of quantum numbers; the view of the particle as a Newtonian object with modifications is flawed; an alternative basis for the classification of the quantum numbers due to Noyes is described; it is compared with the Standard Model.

We have no representation of physical space, let alone the continuum; the conventional understanding of dimensionality replaced by a 3D argument based on the hierarchy algebra; the finite velocity of light necessarily follows from the pure-number fine-structure constant; it leads to a very primitive form of relativity; this is developed; the quadratic forms which appear in the Lorentz transformation as well as in Pythagoras' theorem are discussed; measurement is defined.

The philosophical position of the book is assessed to see how it fits with some familiar positions — mostly ending in "ism": subjectivism; realism; the anthropic principle; constructivism; reductionism; the critical philosophy; positivism; operationalism; particles.

The following sections are included:

• References

• Name Index

• Subject Index