Book/Combinatorial Physics

Bastin, Ted; Kilmister, C. W. (1995). Combinatorial Physics. local page: World Scientific. ISBN 981-02-2212-2. 

I recommend to read also the following books:

1. Analysis and control of Boolean Newtworks by Cheng et al.
2. Principle of Abstract Interpretation by Cousot
3. The Origins of Order by Kaufmann.

Preface

It is nearly fifty years since the authors of this book began a collaboration based on their common interest in the foundations of physics. During that time others have made very major contributions. The fruits of this cooperative enterprise, particularly of the later part of it, are set out here. One problem has led to another. Over that time it became clear that such existing preconceptions are the space and time continua formed an inadequate basis for a physics which has to incorporate a quantum world of discrete character. Here we argue that the impossibility of reconsiliation between continuous and discrete starting points means that we must start from the discrete or combinatorial position. Otherwise the quantum theory will remain with confusion and muddle at its center.

If intuitive clarity is to come from the combinatorial approach it turns out to be hard won because continuum ideas are so deeply embedded in orthodox physics. It has been possible to travel only part of the way but that has been far enough to reveal another positive aspect of the approach. Discreteness is intimately related, according to our theory, to the existence of scale-constants -- those dimensionless constants commonly thought by physicists to be of some fundamental significance. We should therefore be able to calculate these. Here we are able to detail the calculation of one, the fine-structure constant, which Paul Dirac emphasized for much of his life as an outstanding problem in the completion of quantum electrodynamics. Our value agrees with the experimentally determined one to better than one part in $10^{5}$. The calculation of dimensionless constants will bring to mind the name of Eddington, and although his work was the original cause of the author's meeting, and although they agree with him in seeking a combinatorial original for these constants, their mathematical methods, and certainly their calculation of the values of those, have nothing in common with his. This is a book about physics but philosophers will find that some issues -- once their province -- which they thought dead and decently buried, are resurrected to new life here. Notable among these is the place of mind. The great originators of the quantum theory knew that the action of the mind (or the "observer") had to be part of the theoretical structure, but this development has been aborted. In combinatorial theory there is no escape from the issue. In somewhat the same way, since computing is essential combinatorial, people in and around computer science may find our representation of physics more natural to them than it is to some orthodox physicists. None the less it is primarily the physics community we seek to inspire to carry further a project of which this is the beginning.

Introduction and Summary of Chapters

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.

Space

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.

Complementarity and All That

Bohr's attemp 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 incimprehensible.

The Simple Case for a Combinatorial Physics

Physics not scale-invariant; it depends on some numbers which come from somewhere outside to provide abolute 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.

A Hierarchical Model - Some Introductory Arguments

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.

A Hierarchical Combinatorial Model - Full Treatment

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 close 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 arguments.

Scattering and Coupling Costants

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.

Quantum Numbers and the Particle

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 Noyce is described; it is compared with the Standard Model.

Toward the Continuum

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 finite-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.

Objectivity and Subjectivity - Some 'isms'.

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; operatinalism; particles.