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8.4 Process Time

Now that the extensive continuum has a relation of extensiveness defined on it, it is feasible to investigate to what extent the extensive order of places affects the order of events that occur at those places. Now that the extensive continuum can be divided up in relation to any given place by the relations of precedes, succeeds and alternates with, we want to know how this subdivision is related to the temporal order of the actualisings in the different regions.   The `extensive continuum' defined above, it should first be noted, although called `spacetime', has really in itself a temporal component. It is by itself purely extensive, and totally independent of any changes. It is just the collection of all places, including the places of all present and past events and the places possible for all future events. All these places are gathered together into one vast four-dimensional continuum. We did not construct it as a union of space and time, where space is extensive and three-dimensional, and time is one-dimensional and uniformly flowing. Rather, it is the extensive all-at-once aggregate of all places possible. Extensiveness is `all-at-once' or `under the aspect of eternity' because, although events occur each on its own occasion, all places can be given before there are any changes (events) that occur at those places. Although, on the view of time given in the previous section, not all events (especially not future events) can be given `eternally', this need not restrict our consideration of their places. The relations of precedes e between places, and are only between actualities insofar as what is actual is at least possible. These relations therefore can be given and discussed before any time or changes, and hence need to be supplemented by further conditions in order to find any order of events in the places that are related.

What has been done so far is to completely separate in our minds the order of places in the extensive continuum from any order of events at those places. But this cannot be the whole story, for if events were to be completely independent of where they occur in the four-dimensional continuum, then all events (whether past, present or future) would occur asynchronously. They would have no temporal relations, let alone causal relations, between them. Each would just `happen', with no relation at all to the `happening' of the other events. This may between events which are in fact causally unrelated, but in general some kind of natural constraints are necessary to restrain such a free-for-all.

A variety of constraints may be imagined. One suggestion is to order all events according to some uniform serial time. Each event would then occur at one and only one time. This uniform serial order could be identified with some direction of the fourth dimension in the extensive continuum, or it could be distinct from any such dimension. If it were distinct, however, we would be effectively constructing a fifth dimension. This would be a kind of uniformly flowing `hypertime' to order changes in the four-dimensional spacetime. I don't believe this `ontologically extravagant' hypothesis should be accepted without well-founded arguments.

Newtonian time has all events ordered in a uniform serial order which is identical to the time dimension of the extensive continuum. If the metric of this continuum is Newtonian in the manner of the previous section, then the `time direction' is unique. However, as there is considerable evidence in favour of the theory of special relativity, it is unlikely that space and time in fact follow the Newtonian pattern.


No Universal Serial Time

Many philosophers and scientists have argued that the theory of relativity denies the validity of any universal serial order defined by any metric time. These arguments will be examined in more detail later in the chapter, but they may be summarised as follows. According to special relativity, separate observers very often will not agree on the serial order in which several different `acts of becoming' did in fact occur. Such differences arise for events which have `space-like' separations between them.     Because the order of such `becomings' is not invariant for all observers, Grünbaum [1973] and Reitdijk [1966, 1973] would argue that they cannot have been `real becomings'. Grünbaum claims, for instance, that it is only that the various observers `become aware' of the events at their own various times, with each observer's time depending on his or her frame of reference.

I admit that in general several observers do not always agree on the serial or clock order of events with space-like separations. But, I argue, this is a disagreement only between the different clocks and their serial times, and not between the real becomings in themselves. When we look more closely how these serial times arise, we will see that in an important sense they are derived, and do not affect the separate events themselves. In ordinary relativity theory, metric times are derived by considering the observer in relation to the observed action, and analysing this relation to the actual events which the observer uses to make his measurements.   I agree that for events with space-like relations, the distincts according to a metric time of past, present and future are `secondary qualities', as they depend on the relation of the events to the position and velocity of the observer. This means that there is not necessarily any direction in the spacetime continuum for a time axis according to which all events have a unique serial order.

Figure: Causal Connections A line drawn in this spacetime figure indicates a causal connection, and the time direction is vertically upwards. In circumstances drawn, c follows a, d follows c, d e, and e b, but no definite relation holds between events a and b, or between a and e, or c and b, etc.


Local Process Times?

One response this conclusion about the impossibility of any universal serial time, is to point out that this still allows local orderings, or local process times, that might be based on past, present and future relations with regard to local events. By `local events' here, I mean to consider events and their connections only to their causes and their effects. Within relativity, the relation of a cause event p to an effect event q is always what we called `p precedes q' (the `time-like' in relativity theory). This relation has a definite order, and both the relation and its order are not changed by choices of observers' frames of reference. To observe this local order of events, we have ourselves to be one of these cause or effect events. Only then can we be sure that the event concerned was either past, present, or future. Only by looking at the local causal relations can we be sure that one event is definitely earlier or later than another event. (This view has the interesting consequence that we be certain that our acts of knowing are present acts!) Events which are not connected by local causal chains do not necessarily have any relation of past or future defined between them. The set of all events are therefore only partially ordered by the relations of past and/or future, as pictured in 8.4. By `partially ordered' as distinct from `completely ordered', is meant that only some pairs of events will be related, and that there can be other pairs of events between which no definite relation holds.

In this general position, the process of becoming (kinesis) is distinguished from any universal time order, and is regarded as `ontologically prior' to any particular observer's order.     This view has been advocated by Milic Capek (especially in Capek [1971]), following suggestions from Bergson.     Whitehead and Harris (Harris [1965]) have developed similar positions. To quote from Harris:

Time is no more than the metric of becoming, which is the presentational form of the reality which becomes. Capek [1961] explains lucidly how a single space-time interval between two events may be differently measured by two observers in different frames of reference, because they use different metrics (Capek [1961], p. 218). The result is different local times; but they are secondary characters which do not affect the actual process of `creative advance'. In a valid sense, time [a metric] is mere appearance, though the process of events is not. And this process, we should have learned from Whitehead, is one of `concrescence', of continuous realisation of `definiteness', wholeness or form. 8.7

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Prof Ian Thompson


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