Next: 11.3 `Gauge' Invariances Up: 11. Two Stages of Previous: 11.1 Point Events
First there are `free-field propensities' (satisfying equation (11.1)), and these interact by means of virtual events to produce many-body wave functions (satisfying equation (11.2), or its replacement in relativistic quantum field theory). These many-body wave functions then describe the propensities for actual events. Similar descriptions can be used for both virtual and actual processes, which is not surprising, if actual processes arise from actual processes, and in some way repeat them. We then have a kind of `correspondence' between what happens at the two stages, to use a term of Swedenborg .
Actual events can then be selections from within the range of the -function, and which do satisfy the `Principle of Selection' given earlier in this chapter. Actualising events are thus not interactions after all, nor are they point localisations in our four-dimensional spacetime. Rather, they are point localisations in a `tree-structured space' of branches of the -function which do not overlap with each other in the future.
The exact conditions for the production of actual events will be discussed in chapter 12, but it happens very often that quantum wave functions do split up into alternative branches that have little or no overlap with each other ever again. That much is predicted by the straight-forwards application of Schrödinger's equation as we saw in chapter 4: what is not clear in ordinary quantum physics is when (or whether) definite choices are ever made between the alternative branches. We shall see in the next chapter that many different schemes have been proposed. Many of these different schemes are compatible with the general philosophy of nature I have been presenting, so I will not try to decide between those specific accounts, but will give a general framework in which some of them can be possible and reasonable.
We first have to check that the revised application of the concept of `actualising event' satisfies the criteria found essential to this idea in chapter 6. The actual particulars produced by these actualising events, must, for example, be indivisible and hence unextended. This means that places, if defined as `possibilities for actualities' must be unextended points in whatever space they form when put together by their relation of extensiveness.
The actualising events are now proposed to be selection events in the `tree' formed by branches of the Schrödinger wave function as it extends over all space and to future times, and we represent these by discrete branches lines between bifurcation nodes. The events are like points which `cut' the tree structure at specific places, and which select only those branches which follow the cut. We do not have a repetition of our previous problems (when actual events were at points in ordinary space-time), because now, as shown in 11.2, actual events are the selection of branches at specific times. By the Principle of Selection, selection of part of a branch is not possible, so the `space of possibilities for actualities' contains only a finite number of possibilities at each time, that number being the number of branches still present. Thus we have circumvented the previous difficulties of point actualities, not by have actual events over finite regions, but by limiting the choice of actualising at a given time to one of a finite set of alternatives. This may seem a delicate method of avoiding a refutation by experiment, but it has important empirical consequences concerning the possibility (or rather, the impossibility) of dividing actual events into composites of sub-events. If the selection events we have identified are fully and purely actual, then they are the ultimate, indivisible and terminal products of nature. We would call them the ultimate `atoms' of the physical world, if that word were not already used for other purposes.
There can only be propensities for actual events if the Schrödinger wave function does have discrete branches that have little or no interference with each other. This condition does not obtain all the time: when many particles in solids, molecules, atoms or nuclei are interacting with each other, for example, the different internal particles will have wave functions very much entangled with other. It is only after collisions or fragmentations that discrete and non-interfering branches are formed, and actualising begins to be possible. Where there are propensities for actual events, then those propensities appear to be describable by a probability density function, defined along the branches of the wave function, that gives the probability per unit time for a definite selection occurring. The field of propensities can be described by a real-valued non-negative function, in contrast to virtual events and their propensities, where complex-valued functions appear to be required.
In fact, according to quantum field theory, there are some very interesting features of virtual events and their propensities that make them rather more complicated (and interesting) that actual events and their propensities. These features stem from the fact that the space of virtual events is marked not by definite positions, but by equivalence classes of sets of positions, all of which are `essentially the same' as far as the production of actualising propensities is concerned.
Next: 11.3 `Gauge' Invariances Up: 11. Two Stages of Previous: 11.1 Point Events Prof Ian Thompson