Causal images of time
The concept of time is used by humans to make sense of their relationship with the universe. On its own however, time is too vague to be of much use in philosophy or science. Inevitably, it is supplemented by auxiliary concepts such as causality, determinism, fatalism, teleology, finalism, chaos, reversibility and irreversibility, probability, and more. Each of these concepts represents some particular aspect of time considered important in various contexts. In this chapter we discuss some of these aspects in some detail. Irreversibility is discussed in Chapter 22.
Causality is hard to define precisely. It is used as a basis for judgements in law, the allocation of responsibility, the logic of planning, and for dynamical effects in science. Classical mechanics (CM) in the form given by Newton is predicated on the principle of causation, which asserts that ‘nothing happens without a reason’. Leibniz enshrined this idea into the principle of sufficient reason [Kronz, 1997]:
All truths have a reason why they are rather than are not. [Leibniz]
This is an echo of a principle attributed to Leucippus in the fifth century BCE, who said that [Gregory, 2013]
Nothing happens at random but everything for a reason and by necessity.
Causality begs several questions, such as: ‘who has established that something has happened?’ and ‘to what extent is the reason for that happening independent of the observer?’ To understand causality properly, therefore, several pieces of a complex conceptual framework have to be in place: we need the concepts of primary
Images of Time. First Edition. George Jaroszkiewicz.
© George Jaroszkiewicz 2016. Published in 2016 by Oxford University Press.
observer, event, temporal ordering, and contextual completeness. These have been discussed in earlier chapters.
Suppose a primary observer O has observed many instances of some event E, each at a specific time, as measured by O’s clock. Suppose further that O has noted that, prior to each instance of E occurring, an instance of another event C had always occurred at a definite time before that instance of E. Then O might conjecture that an event E could not occur without an earlier occurrence of an event C. O might even conclude that each event C was the cause of a subsequent event E, which would then be interpreted as the effect of C.
The problem is, C and E events could be the mutual effects of some other cause A, as in Figure 9.1(b). In such a case all we could say for sure was that C and E were perfectly correlated: every time we observed an event of type C, we could be sure that E had already occurred, or would occur, even if we did not attempt to observe it.
However, when we look in detail at such scenarios, matters can be more complex than that. Take events happening on macroscopic scales, such as battles. Each is unique, but it is often convenient to ignore what are in context regarded as unimportant differences and invoke a causal explanation for repeated patterns: the Roman Army invariably defeated the Gauls because of superior training.
Locke believed causality is a category (concept of understanding) used to classify experience [Locke, 1690]:
In the notice that our senses take of the constant vicissitudes of things we cannot but observe that several particulars, both qualities and substances begin to exist and that they receive existence from due application and operation of some other being. From this we get cause and effect. [Locke]
The philosopher John Stuart Mill pointed out a fundamental feature of causality [Mill, 1882]:
If the whole prior state of the entire universe could again recur, it would again be followed by the present state. [Mill]
Fig. 9.1 In (a), event C appears to be the cause of event E. In (b), both events are seen to be caused by event A and are positively correlated.
In logic and mathematics, the concept of implication is related to causality in a particular way. Consider two propositions, P and Q. If it is certain that Q is always true whenever P is known to be true, we write P ^ Q. In words, we say ‘P implies Q’. But can we say that P caused Q?
A moment’s thought gives the answer no: it could be that P and Q were themselves the inevitable consequences of some other event R, so that the truth values of P and Q are correlated, but not causally dependent on each other.
Reichenbach devised a notation to express his notion of causality, known as the mark method [Reichenbach, 1958]. We shall translate his discussion into our terms. Suppose E1 and E2 are two contextually complete generalized propositions such that VE1 = VE2 = 1, where V is the validation function introduced in Chapter 2. If E1 is the cause of E2 we write V(E1 ^ E2) =1 otherwise we write V(E ^ E2) = 0.
Reichenbach considers what might happen if E1 changed, perhaps by a ‘small’ amount, to a modified proposition E" and E2 changed to E". Then according to Reichenbach, V(E1 ^ E2) = 1 is consistent with V(E" ^ E-") = 1 or even with V(E1 ^ E") = 1, but never with V(E" ^ E2) = 1.
There are two points here that should be commented on. First, the possible consistency of V(E1 ^ E2) = 1 and V(E1 ^ E-") = 1 allows for the possibility that E1 could be the cause of more than one potential or actual outcome: this can make sense both in classical and quantum physics. Second, the inconsistency of V(E1 ^ E2) = 1 and V(E" ^ E2) = 1 means that Reichenbach regards causes as unique to their effects. This suggests that Reichenbach’s image of time is that the past is unique, because causes are always supposed to precede their effects.