The temporal directionality argument

The first strike against causation in physics may be found in Russell (1913, p. 15), where he wrote:

The law makes no difference between past and future: the future ‘determines’ the past in exactly the same sense in which the past ‘determines’ the future. The word ‘determine’, here, has a purely logical significance: a certain number of variables ‘determine’ another variable if that other variable is a function of them.

Farr & Reutlinger (2013) interpret this passage in the sense that Russell is making a claim on the incompatibility between physics and the time asymmetry of causation. It is not overtly clear what feature of physics exactly Russell refers to that lets him believe that there is no difference between past and future, but taking it to be the time reversal symmetry of physics seems possible at least. Sticking to Russell’s terminology, one could say that in a time symmetric theory the future can be a function of the past just as well as the past a function of the future, and thus that there is no difference between them.

More recently, this argument against a causal interpretation of physics has been stated, though not endorsed, most clearly by Field (2003) and Frisch (2012). For example, Field’s version of the argument can be summarised with the following claims:

(1) “The relation between cause and effect is supposed to have an important temporal asymmetry: causes normally or always precede their effects.” (2) “But at the level of fundamental physical law, it is hard to see any grounds

for the evident directionality of causation. The point is sometimes put a bit contentiously, by claiming that (perhaps with a few minor exceptions) the fundamental physical laws are completely time symmetric.”

3_{A different way to address this problem is the neo-Russellian strategy, according to which there}

are higher-level causal relations in non-fundamental sciences that are dependent on non-causal physical relations (see the short survey in Reutlinger 2014). I cannot comment here on whether the neo-Russellian strategy is effective. In any case, this chapter presents an alternative.

(3) “If so, then if one is inclined to found causation on fundamental physical law, it isn’t evident just how directionality gets in.” (Field 2003, p. 436)4

According to Frisch (2012, p. 314), “the most telling contrast is supposed to be that between the asymmetry of the causal relation and the putative time-reversal invariance of the dynamical laws of our mature physical theories.“ And Price & Weslake (2009, p. 416) ask the question: “Fundamental physics seems to be time- symmetric, in the sense that if it permits a process to occur in one temporal direction, it also allows it to occur in the opposite temporal direction. How could time-symmetric physics yield something as time-asymmetric as the cause–effect distinction?”

As Farr & Reutlinger point out, however, the case is not as watertight as it might seem at first glance. Recalling platitude (TD) from section 3.3.5, the temporal directionality of causation amounts to that the cause comes before the effect, but not the converse. Furthermore, in the quotations above the time reversal symmetry of physics is understood in the sense that every physical process can happen in both temporal directions (a more precise characterisation will be given in the next section). This opens up the following loophole for a causal interpretation of physics. In positive time it might, for example, be true that lightning usually comes before bush fires and also cause bush fires. In negative time, however, the reverse is true and bush fires usually come before lightning. From here it does not follow that in negative time still lightning causes bush fires and therefore contradict (TD), for it is at least possible to have the temporal directionality of causation fixed to the direction of time such that when the temporal direction reverses also the causal direction does. Hence, one can argue that while in positive time lightning causes bush fires, in negative time bush fires cause lightning. It might seem odd to claim that causal connections can hold in the opposite direction of what we are used to from everyday life, but at least it does prevent a contradiction of (TD) in the light of time reversal invariant physics.5

Notwithstanding, a thought experiment similar to that presented in the last paragraph to underpin, and not to refute the directionality argument, has been presented by Norton (2009, p. 481 f.). Norton asks the reader to imagine a world that consists only of two processes. Process A, which can be a scattering event with an initial incoming wave and a scattered wave, and process B that is isomorphic to A, but also temporally reversed. According to the principle of the temporal directionality of causation, for process A the initial wave comes before the scattered wave and causes it. What about process B? According to Norton (2009, p. 482), “using the time order natural to process A, we would have to say that the principle of causality requires the present states of process B to depend upon its future states.”

4_{Field (2003, p. 436) is quite cautious and ads that “it is not obvious that the claim that the}

basic laws of physics are time-symmetric is correct; indeed, the notion of the time symmetry of a law itself is not as clear as it sounds.” Indeed, Field favours the argument from nomic bidirectionality of physics against causation.

5_{I have more to say in section 4.3.1 on how the temporal and the causal direction can be tied}

Norton concludes that this is a reductio ad absurdum for the temporal directionality of causation, since if it applies to process A that causes come before the effects it does not apply for process B and vice versa. However, I do not think that Norton’s argument is conclusive, for prima facie there are two possible ways out. First, one might follow Norton and evaluate both processes using the same temporal direction. In that case, Norton does not explain why one cannot conclude that in process B it is the scattered wave that causes the initial wave. On the other hand, Norton does not give any reasons why, when assessing the causal relations of process B, one should ‘use the time order natural to process A’. Thus, Norton gives no reason that would preclude the possibility that with the temporal direction of process B also the causal direction is reversed, such that for both processes it is true that the initial wave comes before the scattered wave and causes it, even though the processes have opposite temporal directions.6

A stance on causation that would make this move at least implausible, if not impossible, would be hyperrealism about causation. If there is some property that makes a cause a cause and an effect an effect over and above all physical properties, then why should the causal direction be attached to the temporal direction? If in positive time lightning has something that bush fires do not have and that makes them causes, then why and how should this something go over to bush fires in negative time? It would follow that independently of the direction of time lightning causes bush fires, and that they, say, in positive time come before bush fires, but in negative time come after bush fires. However, for several reasons hyperrealism does not seem like a desirable position to take (cf. Price & Weslake 2009). In particular, in this context one might wonder why a hyperrealist should worry about the directionality argument at all. If causation is that much removed from physics, then any concern about reconciling physics and causation seems obsolete.

As a consequence of the directionality argument’s failure in the above interpretation of the time symmetry of physics, the question automatically comes up whether there is a different interpretation in which the argument succeeds. Even though in the above thought experiments time reversibility might have led to two different causal processes, there was no contradiction, since nothing demanded that both processes needed to have the same causal order. As a consequence, Farr & Reutlinger (2013) note that for the directionality argument to be valid the time reversal invariance of physics must be interpreted along the following lines:

(¬TD) No temporal directionality: If in one time direction it is true that event A causes event B and A comes before B, then, by the time reversal invariance of physics, it is also true that the same event B comes before the same event A. This allows for a valid reformulation of the directionality argument:

1. If a process is causal, then, by (TD), it has a unique temporal direction. 2. If a process is a physical process, then, by (¬TD), it has no unique temporal

direction.

3. If a process is a physical process, then it is not a causal process.

In the next section I will discuss more carefully what time reversal invariance is, which interpretation of it supports (¬TD) and why I do not think that it is feasible. But before, I wish to briefly present a discussion between Norton (2007, 2009) and Frisch (2009b,a), which could give reasons to believe that, independently of time reversal invariance, physics is temporally asymmetric.

Frisch (2009b, p. 461) argues for “the claim that asymmetric causal notions play a role in theorizing in physics.” His argument rests on a case study on how dispersion relations are derived in standard physical textbooks. For Frisch, the particular step in the derivation is the condition that if an interaction happens at a time t0, then it

does not have any effect on the waves that participate in that interaction at times t < t0 (cf. Frisch 2009b, p. 463). Frisch observes that physicists often refer to this

condition as the ‘causality condition’ and justify it as being in agreement with the intuition that the cause comes before the effect. Furthermore, Frisch speculates that there is an underlying reason for why physicists think of this as a causality condition that draws on the connection between causation and the fact that we can only intervene on the future.

Frisch himself refrains from inferring any further conclusions in the direction that the physical processes involved in dispersion are causal themselves:

But I do not here want to take sides in the debate as to what metaphysical conclusions we should draw from the fact that asymmetric causal relations play a substantive role in physical theorizing. Theorizing in physics involves appeals to causal constraints, just as it involves positing quarks or electrons, but what metaphysical commitments follow from this is a question I do not want to address here. (Frisch 2009b, p. 461)

Nevertheless, one could take Frisch’s observations as the starting point for an argument that at least in some areas of physics temporally asymmetrical conditions are indispensable and that the temporal directionality of causation can be based on them. However, as Norton (2009) points out, the asymmetry of dispersion relations does not solve the problem that the underlying fundamental theory, namely, electrodynamics is still temporally symmetric and that dispersion relations cannot be rigorously derived from it.

Physicists developing dispersion theory arrive at a general result through a complicated mix of intuitions about how electrodynamical systems behave, the experimental evidence, and more precise computations on artificial examples. They have sought to legitimize that result by appeals to ‘causality’, apparently believing that this calls up a greater body of theory capable of grounding their inference. (Norton 2009, p. 477)

Norton argues, correctly I believe, that the main motivation for physicists to impose an asymmetrical condition is to arrive at a model that is empirically adequate, and not to agree with intuitions about causation; a point that Frisch (2009b,a, p. 490, 471) seems to agree on. On top of that, Norton (2009, p. 478) stresses that what

Frisch calls the ‘causality condition’ is merely the choice of initial conditions. By choosing certain initial conditions, we choose one model out of a set of models that is compatible with the equations of motion. Thus to get the temporal asymmetry it is not necessary to apply a causally condition that lies outside of the theory.7

It follows, that dispersion relations do not seem to give any additional reason to assume that fundamental physical processes are causal. Hence, in his reply to Norton, Frisch (2009a, p. 491) concedes that “Norton is correct in claiming that causal notions are not fundamental in the sense that they play no role even in our classical micro-theories of the ‘inner constitution of bodies’.”

4.2.2 What time reversal symmetry amounts to, or why the argument