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9.2 Propensity Fields

If an actual event A causes an actual event B, then the fact of that causation implies that there was a form of distribution of the power or propensity over the set of possibilities, since, in general, not all possibilities are equally likely. The possibility which is eventually realised cannot just be the one with the greatest propensity, otherwise the competing alternatives with lesser propensities would not have been real possibilities in the first place. Allowing for a distribution of propensities means therefore allowing for a range of possibilities, each of which has some (i.e. non-zero) chance of occurring.

This was the sixth component of the analysis of section 7.2. We can now make this idea more concrete, by using the identification of these possibilities as places in spacetime. Since the `form of distribution of the power or propensity over the set of possibilities' now is seen to be a `form or distribution over regions of spacetime', it can best be represented as a field.

  It could be that powers and propensities have themselves some numerical measure, by means of positive real numbers representing probabilities for example. This field would then, in mathematical terms, be a positive scalar function over a subset of the four-dimensional continuum ${\cal R}^{4}$. In general, however, we do not have a priori reasons to choose that (or any) measure for the propensities themselves. More complicated measures may have to used, provided that some probability distribution can be derived for where the subsequent events are likely to occur.

In general there will be empirical arguments from physics concerning the best measure for a propensity field.   If interference phenomena are to be predicted, for example, then negative (or complex) values of the field will be required.   The Schrödinger equation in quantum mechanics, for instance, uses a complex valued measure to describe the propensity distribution,     and Dirac found it necessary to generalise this to a four-component complex-valued function, in order to describe both electron spins and anti-electrons in the same formalism. Whatever measure or descriptions of propensities may prove necessary, the notion of a field can be used to give the degree of propensity that is operative at each place in a spatiotemporal field.

Philosophically, what is important is that a particular propensity field can extend over many places, with different degrees of propensity at these different places, and not by itself single out any particular place in that region. The propensity field therefore extends over all places at which events `might have occurred', given the actual history of the world up to that point. Of course, one particular place will become selected once an event occurs,   but this selection may well be objectively random in the sense that repetitions of this same history and of this same propensity distribution may result (with certain probabilities) in the occurrence of different events.

Figure: Successive Actualisations of a Propensity Field An initial event A is the production of the propensity distribution shown at process time $\tau = 0$ for subsequent actualising events. After a new event B has happened at at place pAin spacetime (process time $\tau = 1$), then a new propensity distribution is operative. Process time counts actualising events after they have occurred.


To recapitulate on the schema for causation that has been developed: we start considering the causal process with an event A, say, at some place pA in space and time (see figure). The propensities (which are responsible for making occur a successor event to A) therefore extend and endure through the spacetime continuum away from the place pA over places where successor events may occur. The exact spatio-temporal form of this field is given by a general field equation from a theory of physics, along with the boundary conditions that the field must be contiguous with the event at place p A .   Once the propensity field has been formed, it endures until its realisation produces a new actual event B, say, at some place p _ B. If and when that realisation occurs, there are produced further propensity fields which extend from the place pB , and thus endure into the regions of spacetime to the future of B. The whole process is thus started over again. Because the further propensity fields extend away from the place pB , which is only one place in the range of the first field, the realisation or actualisation of the event at pB is what quantum physics calls the `reduction of the wave packet'.   This will be considered further in subsequent chapters.

It is possible to say that the first propensity field becomes another, because the act that is the realisation of the first field is simultaneously the act of forming the second, and because there is a spatio-temporal continuity between the initial and the final propensity distributions.    

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Prof Ian Thompson


Author: I.J. Thompson (except as stated)