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Elementary Process Theory: Axiomatic Introduction and Applications

Friday, 23 September, 2011 - 14:30
Campus: Brussels Humanities, Sciences & Engineering campus
Faculty: Arts and Philosophy
Marcoen J.T.F. Cabbolet
phd defence

In this PhD project, the research question was which fundamental laws of nature would govern the physical
universe assuming that antimatter (such as positrons, antiprotons, and antineutrons) will be repulsed by the
gravitational field of ordinary matter. Thus far, gravitational repulsion has never been observed; however,
several experimental projects are currently being carried out in order to establish the coupling of antimatter
with the earth’s gravitational field.
During the course of research, which was carried out in the form of a Hegelian dialectical process, it became
immediately clear that an observation of gravitational repulsion would pose a problem that the existing
language and assumptions of contemporary physics would not be able to handle: gravitation is then not
what is laid down in general relativity, and antimatter is then not what is laid down in the standard model of
particles and interactions. The main research activity was therefore focussed on identifying what kinds of
entities then exist in the universe and on developing new first principles about the nature of physical reality.
As such, the research activity falls under what Whitehead called “speculative philosophy”, but the end
result transcends the borders of pure philosophy for two reasons: first, because the resulting theory is testable
by the scientific method of Lakatos, and further because it is formalized in mathematical language – as
Cobb put it, “the dominant form of philosophy in the English-language world … assumes that meaningful
communication can occur only in ordinary language.”
The main result of this PhD research is a physically complete ontology of Kant’s noumenal universe,
that is, the universe as it is in itself, apart from how it is observed – the Kantian view that this is cognitively
inaccessible is thus rejected. This ontology then consists of a set of ultimate constituents of the noumenal
universe that are referred to by mathematically abstract symbols, and of a set of first principles – the Elementary
Process Theory (EPT) – that are formulated mathematically by means of these symbols and that
entail the view that physical reality is best understood as a process. It turned out that the usual language of
mathematics, that of Zermelo-Fraenkel set theory (ZF), was not appropriate for the definition of the formalism:
this led to philosophical problems that were both unavoidable and unsolvable. Therefore, a generalization
of ZF, called set matrix theory (SMT), was developed: while ZF uses only sets as terms of the language,
SMT uses matrices with set-valued entries – that enabled a formulation of the EPT in mathematical
language without any problems. For the physical interpretation of the formalism, which is defined by a
number of interpretation rules, some new primitive concepts were introduced, in particular the concepts
‘phase quantum’ and ‘monad’; the latter differs from Leibniz’ notion of a monad. The additional concept
‘binad’ provides a link to existing language: electronic/protonic/neutronic binads are, in existing language,
states of being of electrons/protons/neutrons; the EPT contains an axiom about the composition of these
binads in terms of phase quanta. The remaining six axioms concern the events that take place in the individual
processes: during the course of research it was understood which discrete transitions had to take
place for gravitational repulsion to exist. The EPT is then physically complete: the axioms give a generalized
description of all individual processes in the universe – not just those concerning gravitation – and
with that the creation of all its ultimate building blocks. Constituents such as electrons, protons, neutrons
and their antimatter counterparts all exhibit stepwise motion in the universe of the EPT.
The EPT has been critically confronted with the contemporary foundations of physics, that is, with
quantum mechanics (QM) and general relativity (GR): a formal proof in the language of the EPT is given
that both QM and GR are incompatible with the axioms of the EPT. In addition, the EPT has been compared
with Process Physics (PP) and Whitehead’s Process Philosophy (WPP): while the EPT and PP have
virtually nothing in common, some aspects of WPP agree with the EPT – although, all in all, WPP and the
EPT differ fundamentally with respect to their views on what constitutes an individual process. Furthermore,
several applications of the EPT have been developed: a variety of observed processes has been formalized
in the framework of the EPT, a theory of the Planck era of the universe has been formulated using
the language and axioms of the EPT, and a mechanism for mental causation has been defined that fits
seamlessly in the ontology given by the EPT. These applications demonstrate that the EPT, despite its differences
with existing theories, applies to real world problems.
The main conclusion is that the original research question has been answered and that the results form
an entirely new disciplinary matrix. It remains a challenge, however, to demonstrate that the laws of physics,
known to have merit in some area of application, emerge from the EPT. A research program with that
aim has been mapped out: further work in this direction is thus needed to establish whether or not the EPT
constitutes an advancement in the understanding of the fundamental workings of the universe.