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As discussed in Redhead , one consequence is that any realistic
extension of quantum mechanics will have to use non-local
properties and/or causal connections.
Maxwell  points out that even the very notion of actualising of
potentialities involves some basic kind of non-locality if the
potentialities are distributed in space. This is because only
one actuality can be realised, and the choice of one actualising, in
order to `block off' all the incompatible possibilities, must be
immediately felt in all regions of the potentiality
In quantum physics, this process is known as the `reduction of the wave
packet', and has been the subject of considerable controversy ever since
it was proposed by von Neumann . I am proposing a similar process
here. Proposals for how it could work will be examined in chapter
In the meantime, however, we are concerned with constructing a notion of
time which renders such a process feasible. We are not yet in any
position to discuss wave functions or wave packets, but we can discuss the
actual past-events, and the order (if any) in which they come to be. The
point is that the presence of even restricted kinds of non-local causal
connections renders inadequate the multiple `local process times' of the
One might have expected, independently of experiments in quantum physics, that our actual past-events should all have determinate relations between them (once they exist of course). This is because `actualities' were defined as those particular existing things which were fully determinate in every respect. On this basis alone, we may have expected that there should be definite relations between all these actualities, and if they turn out to be past-events, then we should expect that all these past events should be related in some definite order. This would indicate that there ought to be some kind of `global process time' that goes considerably beyond the `local process times' of the previous section. A global order of actual events would form a complete rather than a partial order, so that for all pairs of events, one of the pair will be definitely (and actually) before the other. The existence of such a global order can be immediately seen to be counter to the usual formulation of the special theory to relativity. Special relativity can either be formulated as expressing the relations between the observations of observers in uniform rectilinear motion, but, as Grünbaum  shows, it can equally well be expressed as the conventionality of distant simultaneity. According to special relativity, there are no intrinsic relations of simultaneity between spatially separated events -- the in 8.5. may be set arbitrarily in the range The existence of a global process time would seem to be directly counter to this arbitrariness. There are several ways in which a total ordering of all natural events could formulated. The actual ordering of events could be
Problems with this scheme arise however, if the universe were expanding
and unbounded, as then different averaging procedures could give different
different results for the centre-of-mass velocity at any given place. This
is because the calculation of centre-of-mass velocity of an expanding
universe presupposes some notion of simultaneity in order to
determine the velocity of distant galaxies. The option can hardly be used,
therefore, to define what is meant by simultaneity and/or
actual ordering of distant events.
The trouble is, that we know of no reasons to select any one such set of hypersurfaces, rather than another, as the basis for the actual ordering of all events. Furthermore, if we did know of a basis to select one such set, this would seem to be counter to the theory of relativity, which requires that all laws of nature must be invariant with respect to changes of velocity and position. It is all very well to argue, as Maxwell  does, that there must be some selection of a set of spacelike surfaces, but some basis for them must be provided.
In the Aspect version of the EPR experiment, for example, the detection events can be placed in a spacelike relation, so that their places alternate with each other. Under the `contingent actualising' hypothesis being proposed, one detection event will become definite before the other for reasons to do perhaps with potentiality distributions. This first event will non-locally determine the potentialities for the second event's outcomes, even though the second event is in a spatial relation with the first, because it is a basic feature of potentialities that only one outcome is possible for every event. All events have a definite order, and according to this actual order, earlier events can affect the propensities for later events with which they are correlated.
The laws of physics are symmetric and invariant with respect to changes of velocity and position of coordinate frames, but this symmetry is broken once actual events start occurring. Other examples of `spontaneous symmetry breaking' are well known in physics, such as the Weinberg-Salaam theory of the electromagnetic and weak interactions. After spontaneous symmetry breaking, symmetric laws are broken by the requirement that something actually happens. Then, as we shall see in the present case, what has actually happened in the past propagates its effects to influence present symmetry breaking.
Spontaneous symmetry breaking in physics is often illustrated by the example from elementary classical mechanics of a ball on the top of the `Mexican Hat' shape shown in 8.5. The initial state of the system is clearly symmetric under rotations about the vertical axis, and there is no predetermined direction for the ball to move, because gravity acts only in the vertical direction. Yet, the initial state is unstable, and the ball will eventually fall in one direction or another. As it loses energy through friction, it will eventually come to rest somewhere in the rim of the `hat'. Its final situation there is stable, but no longer has rotational symmetry. We say that the rotational symmetry in the underlying forces is `broken' by what actually happens. The actual position in the rim is purely random, and cannot be predicted by the theory. The actual outcome has no deep significance, yet it influences what happens from then on, for all times.
Next: 8.6 Necessary and Contingent Up: 8. A Theory of Previous: 8.4 Process Time Prof Ian Thompson