The Origin of Discrete Particles

The following sections are included:

• Foreword

• Acknowledgments

• Contents

The method for physics put forward in this book is constructive. One may alternatively say that it is a process theory. In it one does not imagine the space and time continua as existing outside the theory and giving us a universe of objects already distributed in these continua to start from. All this has to be constructed…

A hierachical theory presented in Chapters 6 and 7 is prefigured. In it, contact with the experimental world is through elementary interactions which appear as the strengths of elementary particles. Space is combinatorial and not absolute — or existing beforehand. Leibniz was the pioneer of this combinatorial approach. Computing models provide the connectivity of this relational space (this term for it used by Leibniz).

History of the particle concept, Democritus, Aristotle, Epicurus. Reality or hypothetical view? Is there a limit to cutting things up ever smaller? Newton represented the unphilosophical mechanical view that dominated classical mechanics. Dalton confirmed the realism. Planck imposed the discreteness mathematically. Logical incompatibility of discreteness and this classical picture led to the quantum theory of 1926 based on the state/observer principle. Schroedinger's and Dirac's views of this principle. An entirely new attribute of the particle appears with 'exchange'.

Eddington's program of finding values for dimensionless constants. Symmetry of spatial dimensions invoked in answer. The quadratic group S fundamental. Complexity had to be introduced by putting together a multiplicity of groups. Association of two, gave enough complexity to define electromagnetism. No metric used. Multiple feedback models constructed (Gordon Pask) to provide a metric. Parker-Rhodes formalized these principles and discovered the algebraic hierarchy with its striking progression of numbers.

A hierarchy of levels used the idea of any one level being constructed out of the operations at the preceding level. Parker-Rhodes gave this idea digital or combinatorial form. The unit for such physics was the discriminately closed subset. Characteristic numbers emerged. These provided the setting for particles.

The inverse fine-structure constant is calculated as 137.036011393…, agreeing to better than one part in 10⁷ with the latest experimental value, 137.035999710…. The statistics that generates the base number 137 from the process theory is progressiviely refined in a long calculation, the details of which are set out at length in two notes at the end.

Contrast of conventional prescription by laws and the sequential picture. Process has no sudden jump at which there is physical interpretation. Interpretation is there from the beginning and builds up with the mathematical equipment available. In process one has to start independent constructions or duplicate them. Time first and space later and less fundamental. The levels incompatible with all-or-none interpretation. Pace Parker-Rhodes. He didn't realise his own levels demanded a new philosophy. Significant numbers characterise the levels. In fact cumulative summation entailed process. The numbers come from the discrimination algebra and are only derivatively connected with space structure. The changes in level enable contact to be made with conventional physical theory provided that they can be identified with the idea of a physical field. The increase in complexity of successive levels has to go with increase in descriptive power of the fields. In fact the most important increase is the introduction of electromagnetic fields. The assignation of the coupling constants to fields is done elsewhere.

High energy particle theory logically prior to space and time and to non-relativistic quantum mechanics. Classification by symmetries, the quark model entirely consistent with the process algebra (transverse construction). Charge and spin. The weak interaction.

Our picture essentially discrete as is quantum theory. Based on the idea of discrimination. We look at the opposite (continuum) picture. A binary relation is essential to introduce space. This relation produced not by continuing the construction process but by repeating it. This introduces "pairs" of elements, thus departing from the construction that leads to levels and to an identification of particles using the numbers that characterise the levels. The pairs of elements make it possible to regard the second level basic structure as exhibiting three dimensionality.

Summary of historical views. Changed view of perception in quantum physics and the 'observer/state' philosophy. The process theory requires a change; there is no stage of perception of a thing separate from its construction. Many constructions compose the perceived world. Space (as distinct from the sequentiality of time) arises from the multiplicity of constructions. The passive observer has no place. Such a view accords with that of Leibniz for whom the physical thing was the appearance of a collection of monads. The paranormal and pan-psychism have to be allowed as possible aspects of the world since they are not excluded by our principle.

The state/observer philosophy fails to provide the fundamental place for discreteness of the particle that our theory requires. It is inconsistent as a basis for quantum theory. The numerical successes of quantum mechanics with spectra are combinatorial in nature — not a new dynamics. Process Theory begins with the identification of the fine-structure constant and others which derive from the process algebra. The discrete nature of energy characterises the quantum theory. A summary of quantum theory is given so that its place for the discrete can be set beside that on which 'process' is developed. Planck's original formulation can only be correct if energy = hν. The development of quantum theory from this beginning is traced through the Rayleigh-Jeans Radiation Formula and the Bohr model of the atom. Schrödinger's influence is described : he was dissatisfied with the discrete jumps of the Bohr theory and proposed continuous wave-functions. A fundamental alternative was introduced by Heisenberg which reintroduced discreteness through a new vision of mechanics in which observable changes alone were to be admitted in theory construction. These principles are applied to the harmonic oscillator. Attempts to provide explanations of the resultant difficulties. Only Bohr's discussion of sufficient depth but even this proves inadequate.

This chapter title is taken from the book by Martin Rees. The six numbers discussed by Rees are seen by him from the point of view of cosmology. Why should they appear in microphysics as well? The numbers are dimensionless and their origin unknown. Rees lists them. By using the process method of this book they can be calculated. One of the numbers is interpreted by Rees as a measure of the 'ripple' or deviation from isotropy.

Quantum theory and relativity clash. Incompatibility of continuum and discreteness. Our theory of the particle and of the dimensionless numbers that shape the categories of particles, requires us to start from the quantum end to get to the desired synthesis.

The following sections are included:

• References

• Index