All scientific theories are set against some
background of general ideas. A.N.Whitehead emphasised this point
and stressed the supporting role that the background scheme of
ideas has in the development of theories. He also underlined the
fact that such ideas are often unacknowledged. Even those who rely
on them often do not realise that they exist, or the powerful
influence they exert. With this in mind, it is not impossible to
gain some picture of the types of background ideas which guided
the imagination of thinkers from Galileo to Einstein.
This is especially the case with respect to
space. Space concepts almost never extend beyond the infinite
extent of fixed, motionless and flat space. Einstein was the first
to venture into new territory, beyond the Newtonian model, with
curved spacetime and its Gaussian trajectories for moving bodies
in a gravitational field. Others have proposed different spaces,
including string theories, but they have to explain away invisible
dimensions and other concepts which clash with common sense and
brute facts. These have usually required complex mathematical
treatments, often at the Planck scale of space and time, which
obscure any relationship to the real world.
Background concepts to the Discrete
Theory of Elementary Particles
Some of the newly embraced ideas are found in
the work of A.N.Whitehead and others following the Einstein
revolution. Those ideas are not readily summarised in a few
words. The key features of the doctrine of organic realism, as
Whitehead named it, do not immediately find easy acceptance by
those new to its concepts. His metaphysical scheme was couched in
an extremely general form, in order to find application in all and
every aspect of human experience. Both its generality of
presentation and the scope of its intended extension have been the
cause of its narrow acceptance among scientists and philosophers
alike. Scientists want science to be science—not philosophy or
theology.
The adopted elements of organic realism can be listed as follows:
• Physical reality, with which we are familiar, can be analysed in
terms of events
• Events are the fundamental or founding elements of microscopic
reality
• Enduring objects, such as electrons, are each series of such
events—matter is event-like
• Each event is a complete and isolated occurrence—it happens then
vanishes
• Notwithstanding their completeness and isolation, events inherit
their characters from other events—they are dependent upon other
events
• Space and time are relational—they are not substantial—they are
derivative of the objects they relate. Objects come first—space and
time follow
An analogy with the analysis of microscopic
reality as events, is the action on a cinema screen. It can be
analysed as a series of separate, still pictures which appear one
after the other on the screen. Nothing moves in the movies in the
fundamental sense. Cinematic action is derivative of
motionlessness.
In the present scheme, the distinction between action and its
representation is crucial. Twentieth-century physics focuses
almost entirely on representation, to the extent that what lies
beneath all but falls out of sight. The laws of physics are
expressions of the regularities of Nature. And the regularities
are expressed as mathematical relations among phenomena. Modern
physics is almost completely reduced to the mathematical
representation of phenomena, from which derive its laws.
Post-modern physics, begun in 1900, increased the level of
complexity of the mathematics by its introduction of symmetries.
The action which lies behind the symmetry is another matter.
Feynman put it in a nut shell when he wrote:
"One might still like to ask: 'How does it work? What is
the machinery behind the law?' No one has found any machinery
behind the law. . . We have no ideas about a more basic mechanism
from which these results can be deduced."
—R. P. Feynman
The discrete theory is entirely concerned with
what Richard Feynman refers to as: "machinery behind the law" and
not its representation(s). In addition to the motionlessness of
the action behind phenomena, its energy is treated without
reference to its quantification. Thus, the need for a Hamiltonian
approach vanishes and with it a reliance upon energy-centred
mathematics. By treating space and time as properties of systems
they become distance, direction and duration and not objects in
their own right. Instead of equating the treatment of their
representations, constraints applied to a particle's internal
duration are the same as those applied to its internal distance
(diameter). For fully discrete particles time is a physical
variable. Individual particles have various durations.
Energy differences among the particles of the
standard model are not of primary importance in the discrete
scheme. The Pauli principle is obeyed naturally by interacting
particles which differ in their energies but are distinguished
by its conjugate relative—time, expressed as duration internal to
the event. By contrast, a difference which is of great importance
is that between the application of the terms 'positive' and
'negative' to the physical quantities, energy and electric charge.
Pauli and Dirac each believed that 'positive energy' and 'negative
energy' could not both be physically real. They naturally opted
for the reality of the former and the non-reality of the latter.
The problem finds a solution in the discrete scheme by way of an
alternative to the usual mathematical means of interpreting
'positive' and 'negative' as opposites of
one another.