 
Next: 10.4 Measuring as Actualising
Up: 10. Quantum Substances
Previous: 10.2 Probabilities and Propensities
Subsections
One feature of the present account of substances is that they are not
necessarily located in small volumes of space, as, for example, the
corpuscles or `particles' of classical physics would be. The
propensity fields that have been defined do not even have any special
`centre' distinguishable from all the other places in the field.
They have no centre which could be regarded as the `true substance',
so that the surrounding field could be regarded as just the `sphere of
influence' of the central substance.
This was Boscovich's conception, and it slowly percolated into physics,
resulting in the `dynamic matter' of the midnineteenth century. This view
is best summarised by the aphorism ``No matter without force, no force
without matter''.
Our propensity fields, though, have no special continuing centre: the only
`point source' which could perhaps be identified is the source
event, which must have a definite location in space and
time. The field is therefore only localised very briefly, if at all,
at times just after this source event. The `continuants' we define are
thus occasionally, but never necessarily, strongly localised. For most of
the time they have significant spatial extensions.
Various reconsiderations to ideas of particles have been suggested by
quantum physics have over the last sixty years, but for the most part come
fitfully and in scattered parts of which few physicists or philosophers
were fully aware in a critical sense.

 1.

Margenau [1950, 1954] advocates a `latency interpretation' of quantum
mechanics. In this interpretation, what is real is the state function
function, whereas the classical state observables, such as position,
momentum or energy may be said to be latent in , in the
sense that their values emerge only in response to measurement. The
distinction between primary and secondary qualities is superseded by that
between `possessed' and `latent' qualities or observables, the former
exemplified by mass or charge, the latter by the observables with which
the quantum theory of measurement is concerned. These later ``are not
`always there', [but] take on values when an act of
measurement, a perception, forces them out of indiscriminacy or latency.''
In the theory of propensities, Margenau's `possessed' qualities are
parameters which describe strengths of propensities, and his `latent'
qualities are parameters which describe the outcomes of operations of
propensities.
 2.

Heisenberg further notes^{10.4} that
what a typical physicist of today tends to think is rather close to
Aristotelean `potentia', even if unwittingly. The meanings of words such
as `particle' have moreover gradually changed in these sixty years.
 3.

Kaempffer [1965], for instance, after pointing out the `erosion of naive
pictures of particles', goes on to suggest that the word
particle stand for a quantum mechanical state [a wave
field], characterised by a set of quantum numbers, which is
associated, in principle, with an identifiable event such as the momentum
transfer in a ``collision''. This conception of a particle (as a wave
field associated with a definite event) has come a long way from the
corpusclar theory, and is remarkably similar to the present account of a
continuant as a propensity field which extends over the various places
possible for actualising events.
 4.

Müller [1974] is trying to formulate an objective interpretation
that is materialistic as much as is possible. He interprets probabilities
in terms of `potentially possible events', though he `doesn't wish to
establish any ontological order'. He wants to describe objects while they
are not being measured: `the premeasurement condition of the object can
be characterised only by the probability distribution of the potentially
possible states'
^{10.5}
.
Wave Behaviour?
The point to note is that the continuantfield does not have a
fixed spatial size. Sometimes it behaves more like a spreadout wave, and
when at other times it interacts, it behaves like a localised particle.
In fact, propensity fields can have practically any extensive shape over
the places that are possible for it, as they are subject only to some
field equation. We can allow that propensity fields are described by
Schrödinger's time dependent equation, including the interaction
potentials. This then allows them to propagate in interesting manners
around obstacles or potentials which would stop any classical atoms. They
can even tunnel through barriers, as the probability for a definite
interaction may be reduced but nonzero. It becomes reasonable to expect
the diffraction, interference and tunnelling effects we know in quantum
physics from the solutions of Schrödinger's equation.
Particle Behaviour?
On the basis of our account of propensity fields as continuants:
 There are no such things as small particles like corpuscles with
definite properties.
 Nor are there such things as small particles with uncertain or
indeterminate properties.
 Measurements are not the process of assigning values to properties of
particles
^{10.6}
, even if we allow that they are `peculiar particles' in not having
definite properties at all past times.
 Nor are measurements the momentary production of particles
with definite properties for that moment.
To believe any of these is to believe that somewhere, as it were hidden
away behind the propensities, there really exist particles waiting to
appear. This is not the case. Questions like `Where is the electron and
what is its speed?' have no answer, because there never exists such a
thing as a small corpuscular electron. The only things that exist are
propensity fields and the actualities they produce. Propensity fields are
not like vague, indeterminate or smearedout particles, but are perfectly
definite entities in their own right. It may not be determinate in advance
which actualities a propensity field will produce, but that does not mean
that the propensity field is any the less real or definite when considered
as a thing in itself. Its field structure can be described using perfectly
definite mathematics. Its existence is as real and substantial as any
existing object. In fact, as we saw in chapter
9,
propensity fields are the very substances out of which all things are
made! Nothing can be more substantial than them. It is only given all
this, that we can follow Kaempffer above when he redefines the meaning of
the word `particle' to refer to (something like) propensity fields!
We may appear to be using particle ideas when we talk of `observables'
such as position, energy and momentum. The meaning of these concepts seems
to be irrevocably connected with the classical ideas of particles as
atoms. In fact, position, energy and momentum can be given selfsufficient
definitions as `variable' properties of propensity fields. They are
variable, in the sense that they vary across the extent of the field.
`Position' obviously varies across the field, as fields were initially
defined in terms of the range of places or positions within their range.
If the field is a function following Schrödinger's equation,
then the probability distribution of `position' at any given time is
proportional to
`Momentum' is a `variable' which also changes according to where you are
in the field. If the field follows Schrödinger's equation, then
the `local' component of momentum in a given direction is simply the
logarithmic derivative of
in that direction:
Similarly, the local value of the `energy' variable is the logarithmic
derivative of the function in the time direction of the extensive
continuum:
The socalled `classical variables' of position, momentum and energy are
thus functions or derivatives of the propensity distribution at each
point. If it were to actualise at that point, then those derivatives can
be carried over to the new field that is formed after the actualisation.
It is also possible to define mean or expectation
values for the variables of position, momentum and energy, by averaging
with appropriate weights over the whole field. Thus a mean position
mean momenta and a mean energy
can be defined according to
The values of
for the whole
quantum substance are only defined in this mean or
secondary sense, by averaging local logarithmic derivatives
over the extent of the propensity fields.
Complementarity?
The conjunction of an extensive field with some actualising event
also corresponds, I believe, to what Niels Bohr has called^{10.7}
the basic `quantum phenomenon', being an `undivided' and
`closed' occurrence. It is `undivided' because between the
source and realising events is a single extensive propensity field, and
not any intervening actual events which could constitute some kind of
unknown connection. It is `closed' because once a place in a
propensity field has become realised, the field no longer exists: its
history is closed. Bohr's `complementarity' of the wave and
particle aspects of the quantum phenomenom arises because although a
propensity field can be regarded as propagating through space and time
like an oscillating wave and as obeying a wave equation, it is in fact a
single field which can produce only one actual event. This event must be
at one definite place, just as a stronglylocalised particle would
produce. If we were not aware of the notion of a `distribution of
propensity for a definite event', we would be confused because
sometimes the continuant behaves like a wave, and sometimes like a
particle.
This quantum substances are capable of acting like a wave, and
capable of acting like a particle, as Bohr's complementarity
asserts. Once it is determined, however, what events actually
occur, then, at each time, a quantum substance is quite definitely
either a wave or a particle. At any given time, it
is either a field (with wavelike patterns), or undergoing a localisation
event (with a sort of particlelike localisation). It in fact
never behaves like a traditional `corpuscle', in that it never
has a localised extension which is constant for any finite (nonzero)
duration. This is because the localising events (as the production of
purely actual pastevents) have no finite and divisible duration.
TwoSlit Experiment
Consider the twoslit intereference experiment with beams of electrons.
The emission of electrons produces a field of propensity that extends
through space (in the direction of the beam) and endures through time.
The exact form of this distribution will be governed by something like
Schrödinger's timedependent equation. It will have wavelike
characteristics according to the variation of momentum (see above) in
different parts of the field.
As in Maxwell [1988, p. 16], when the
electron field overlaps with the field of the twoslitted screen,
either the electron is absorbed by the screen and there is an
actual event (an instantaneous, probabilistic collapse of the wave
packet), or the electron wave packet passes through both slits
towards the photographic film. In that case, the electron field extends
across in the intervening space, and the parts of the field that came
through different slits will interfere with each other constructively or
destructively in a wavelike manner. Eventually the recombined
electronfield will overlap with the photographic plate, more specifically
with all the photographic grains in the plate.
An actual event can necessarily occur on interaction with only
one of these grains: this amounts to a reduction of the wave
packet to a highly localised form trapped in the grain. Thus, one
particular grain is definitely exposed, and none of the other grains will
be exposed. If the whole process is repeated with many electrons over a
period of time, then a statistical distribution of exposed grains will be
built up according to the probabilities resulting from the propensity
distribution of the recombined electronfield.
The exact sufficient condition for an actualising
event will be discussed in chapter
12;
Maxwell proposes that is the difference in energy between the exposed and
unexposed grains which triggers the actual localisation of the propensity
fields.
Superpositions and Mixtures
Until an actualising event occurs, the propensity fields may well extend
over a wide range of possibilities. In the language of quantum mechanics,
we would say that the quantum system is in a superposition of these
different possibilities. After an actualising event occurs, then only one
possibility can be realised for each propensity field (each quantum
substance), and there will be different probabilities for the different
outcomes. What this corresponds to in the language of quantum mechanics
depends on whether we know what the actual outcome is. If we do know, then
a measurement is said to occur.
If we do not know the particular result, but only that some
definite outcome did obtain, then the system is said to be in a
statistical mixture of the different possibilities. The
statistics arise here because of our ignorance as to what actually
happened.
It would appear in summary, then, that the present conception of substance
is able at least qualitatively to account for several of the features of
nature that have been captured by quantum physics, and which are
mysterious or impossible in classical physics. We can see how there might
arise a `waveparticle complementarity', indeterminacies, objective
probabilities, diffraction, interference and tunnelling effects.
Next: 10.4 Measuring as Actualising
Up: 10. Quantum Substances
Previous: 10.2 Probabilities and Propensities
Prof Ian Thompson
20030225
