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A Discrete Theory of Elementary Particle

This and the following pages presents some of the ideas and consequences of a project to recast, from a perspective which is fully discrete in both space and time, the central elements of twentieth-century microscopic physics that are usually assumed to inhabit a plenum of continuous space and time. It is not a simple extension of continuous physics as it has developed since Newton. But it does deal with the three most important constituents of the real world which form part of the standard model of particle physics—electrons, protons and neutrons, together with their bosons. 

Like the standard model, the project seeks to unify descriptions of microscopic reality under a single principle. Unlike the standard model, the present approach relies upon qualitative models which tend not to produce accurate predictions. It is sometimes argued that quantitative predictions are the hallmarks of significant theoretical advances. However, there is also room for theories that unify, under a single principle, apparently unconnected laws of nature—explanatory power before quantitative predictions.

The project is not in the mold of mainstream physics, it does not, in the words of Richard Feynman, put the information in mathematical form’, or ‘guess the equations’.*  It is physics beyond the standard model.

A Scenario Beyond the Standard Model
Modern physics is entirely dependent upon representing phenomena in the language of mathematics. For Galileo and Newton the mathematical formalism brought crucially important precision to the exercise of natural philosophy. Its growth ever since has become a self-sustaining edifice with a legion of devoted adherents. In one sense, physics has engendered enough mathematics over the last century to supply a multitude of new theories. Qualitative models, by contrast, have generally been at or beyond the margins.

The mathematical approach which is commonly of central importance in dealing with the problems of the microscopic world, for example the quantum formalism, brings with it the unavoidable assumption of continuity. Here, an alternative approach is the aim. There is no assumption of continuity of space, time, motion or elementary particles.

The present approach is to move away from the set theoretic framework to a more physical scheme. However, that does not mean that the successes of continuity physics are to be rejected out of hand; rather, they are to be interpreted without the use of real or complex numbers. Such an example is the set of consequences of the Dirac relativistic equation for the electron. The equation is rightly regarded as one of the supreme achievements of the quantum revolution. Its consequences include: (1) the energy of the electron may be less than zero, (2) it moves at the speed of light and (3) its essence is equally reliant upon time and space. None of these aspects of the quantum electron can be accommodated in a real world of continuity.

The present project also begins from the ground-breaking discoveries made by science in the first quarter of the twentieth century. It is constructed from the vantage point of the beginning of the twenty-first century, from which it can be seen that those early successes still lack a satisfactory physical resolution. The theory takes quantum mechanics and special relativity with it. They are both crucial components in the present approach to the discrete understanding of elementary particles. Perhaps not surprisingly, the analysis of discreteness reveals an underlying process that is absent from the physics of continuous elementary particles.

Most attempts to extend the twentieth-century paradigm of microscopic physics into a process framework have begun with established physical theoretical constructs, such as quantum field theory, and attempted to reinterpret them as process physics. That has not generally proved very satisfactory and seldom led to a clearer understanding of microscopic phenomena. 

The method employed here begins with the development of the concept of an event within a framework employing as few assumptions as possible while complying with special relativity and standard quantum mechanics. Out of that grows a discrete interpretation of microscopic physical reality. Quantum mechanics and special relativity become reconciled with one another in a satisfying though somewhat unexpected manner in which the distinction between action and its representation is crucially important. Action precedes its own representation. That distinction brings with it significant explanatory power.

The question of how physics can move beyond the standard model to a new paradigm has not yet been answered. Richard Feynman frequently puzzled over the problem and was aware of the unknown nature of the territory that lay ahead. The following quote is particularly thought provoking: 


* “I am sure that history does not repeat itself in physics . . . The reason is this. Any schemes—such as ‘think of symmetry laws’, or ‘put the information in mathematical form’, or ‘guess the equations’—are known to everybody now, and they are all tried all the time. . . . the answer cannot be one of these . . . There must be another way next time.” 
                          —R Feynman “The Character of Physical Law” p. 163.

Is this a clue to the way forward, beyond, though still connected to the elementary particles that comprise the atom, but with less reliance upon mathematical representation and symmetry principles?

The new theory requires a new quantum variable—one which complements or governs energy in its various forms. Order is that variable and it is the central element in the new theory. Beginning with nineteenth-century thermodynamics, it is properly defined and given the status of a physical quantity comparable with that of energy. Order is the physical content of the rather vague term 'potential'.

Any theory of elementary particles which claims to relate to the real world must clearly set out its concept(s) of space. Unlike string theory which favours spaces of the de Sitter type, in the present scheme flat Minkowski spacetime grows out of a spaceless and timeless precursor via an intermediate Weyl-like spacetime. This makes the theory background-independent, not unlike that sought by the loop quantum gravity project. The objects of the theory, which are the component parts of the atom, are only intermittently imbedded in a spacetime background.

Ideas about the physical world do not just grow into theories in a vacuum; they need a prior background of ideas. They need a foundation which comes in the form of other ideas. They are often the product of an earlier paradigm but it is with their help that new theories develop. 

Quantum mechanics comes in several interpretations. In some ways the different interpretations do not matter. That is not the case with the new theory; the quantum interpretation does matter. The present scheme requires the original interpretation of Bohr and Heisenberg, but without any role for an observer.

The basic claim for the new process picture of reality is that it does make a significant contribution by offering an alternative slant on how elementary particles may be understood. It makes the action as it happens the focus of the analysis instead of its representation which is necessarily a consequence of the action. When the Dirac electron is interpreted in the process framework, electrodynamics becomes a discrete process. A surprising result of the theory is that the behaviour of the electron is both quantum mechanical and gravitational—discrete quantum gravity.

The discrete scheme is applied in detail to the atomic nucleus. The chief result of that analysis is a new theory of nuclear structure. The theory is developed around the isotopes of hydrogen and helium and leads to a four-cluster structural model of the nucleus. The new model is an extension of the existing nuclear cluster concept. The discrete model correlates well with a number of light nuclear phenomena.

Comments and questions are welcome to pjf@it.net.au

© Peter Fimmel 2002-2009

Last page update 21/04/09