Simultaneous Causation

To characterise causation in accordance with the third law of motion not only challenges the ontological priority of the action. It also requires us to think of causes and effects as occurring simultaneously. The idea is not new, but is controversial even though recently it has been gaining in popularity. Kant accepted that most effects are simultaneous with their causes, which caused him some worries about how to understand the ontological priority of causes (1787: B233-56), and today this view is championed by authors like myself, Michael Huemer & Ben Kovitz (2003), and Mumford & Anjum (2011: Ch. 5). Like myself, Huemer &

Kovitz appeal to the way physics describes interactions, and Mumford & Anjum partly appeal to common-sense examples of the kind Kant suggests, and partly to Huemer & Kovitz’s interpretation of physics. I think we are thus in very good agreement. There are plenty of objectors though. Bunge’s objection to interaction, previously discussed, is an objection to simultaneous causation, and more recently we find Robin Le Poidevin (1988) and Tobias Hansson Wahlberg (2017) attempting to prove that causes and effects cannot be simultaneous, because it would entail that things will be in two incompatible states, and/or violate the conservation of momentum. Hansson Wahlberg explicitly relates to myself, Mumford & Anjum, and Huemer & Kovitz, as well as to Le Poidevin.

Le Poidevin appeals to what he calls the principle of reciprocity, ‘a necessary part of any cause is itself affected as a direct result of that cause’s bringing about its effect’ (1988: 152), which Jonathan Bennett calls the ‘Balance Principle’, i.e. ‘in any fully intelligible causal transaction something gains what something else loses’ (1974: 59), and says that this has been part and parcel of the pre-Newtonian mechanics of Leibniz and Descartes. Le Poidevin illustrates the consequences of the principle for interactions between two objects A and B: ‘For any A and B, if A’s being F at time t causes B’s being G at t' then A is no longer F at t'’ (1988: 155). The core idea at play is really that causation is the transmission of something from an Agent to a Patient, and that the Patient’s gains must be equal to what the Agent loses, otherwise something has been added out of nothing or completely annihilated (depending on whether B gains more or less than A loses). Having that understanding in mind, Le Poidevin attempts to show that a contradiction ensues from the idea that causes and effects are simultaneous:

Consider the following example of a moving billiard ball A’s striking another billiard ball B, which until then was stationary. As a result, both balls are in motion. At the moment of the encounter, A’s momentum was MA. After the encounter, A’s momentum is MA* and B’s is MB. Clearly, MA* must be less than MA: A cannot have brought about movement in B without a reduction in its own momentum (otherwise momentum is not conserved). Now A’s momentum at the moment of the encounter is a necessary part of the cause of B’s subsequent movement. So if cause and effect are simultaneous, then A’s having momentum MA must be simultaneous with B’s having momentum MB. But if B has momentum MB, then A’s momentum must be MA*. So A’s momentum, at the time of the effect, must be both MA and not MA. Since this is absurd, causation cannot be simultaneous in this case. What happens rather is that at the time of the encounter, A’s momentum is Mv and at times thereafter, MA*.

(Le Poidevin 1988: 157-8)

In short, the argument is that if causes and effects are simultaneous, then A must have MA simultaneously with B having MB, yet must also simultaneously have lost MA to have caused MB.

Hansson Wahlberg argues in exactly the same way, but instead of describing the consequence as a contradiction he argues that it entails the doubling of momentum, which is a violation of the conservation of momentum:

Now, assume first, for simplicity, that the billiard balls are perfectly rigid and that the collision is instantaneous, occurring at an instant of time t. Then, if a’s momentum is passed to ball b at t- b acquiring the momentum (the effect) simultaneously with a being, for the last time, in possession of its momentum - the sum total of the objects’ momenta is doubled at t. The consequence is that the law of conservation of system momentum is violated at t.

(2017: 113-14)

My objection is that both are using an example clearly intended to conform to classical mechanics, but describe it in terms of the philosophical two-place model involving a conception of causes and events as instantaneous Kim-style events in which one transmits a quantity to the other, which I don’t think is suited to the Newtonian understanding of what happens in interactions. That is, we are given MA as the cause, i.e. the state of A when it begins to exert an influence on B and are supposed to accept that the exertion of influence can be completed instantaneously. And we are given MB as the effect, i.e. the result of a change in momentum instead of the change of momentum itself. It is true that the quantity of momentum can be calculated for an infinitesimal timepoint, but that doesn’t mean that we should understand the exercise of an influence or a change in momentum in terms of instantaneous entities. Here I am with Glennan (2017) that causal realists must assume causes and effects to be activities that take time rather than instantaneous states.

I propose we should understand the interaction as follows. Assume A and B have momenta MA and MB at the instant t at which A and B come into contact. From that moment on A and B begin to mutually exert a force on each other, and simultaneously their respective momenta begin to change and continue to do so as long as A and B mutually exert an influence on each other. At no point in time is it the case that A and/or B have and do not have a given momentum MA*/MB*.

The key thing is to realise that the claim ‘causes and effects are simultaneous’ does not mean that the cause and effect are completed instantaneously (that only follows if you treat causes and effects as Kim-style events). The idea is instead that the exertion of an influence and the production of a change occur simultaneously but over a temporal interval, producing a succession of states (see also Huemer & Kovitz 2003).

Now, while physicists never forget to mention that interacting objects mutually exert forces on each other, they primarily explain interactions in terms of unidirectional transferences of quantities from one object to the other. In accordance with my earlier criticism of the transmission theory in Chapter 3, I believe this understanding is ontologically inadequate, even though it offers a useful method for calculation that usually isn’t misleading. The problem is that it doesn’t generalise to all the cases. It only works in cases that intuitively fit to an Agent-Patient interpretation but fails in symmetric interactions, such as when two identical billiard balls, moving with equal speed in opposite directions, collide head on. They compress on collision and are then pushed off again in the opposite direction to the one they had before, but neither loses momentum while the other gains. Both equally change their direction of motion. How are we to understand the change in terms of transference of momentum in these cases? We have a choice between thinking that each transfers equally to the other (momentum swap) or we assume the interaction only results in a change in the direction of respective momenta (or change in the quantity in asymmetric cases), but not really that momentum is transferred. I think we should let the concept of force do the work it was initially meant to do, notably to explain why colliding bodies change the momentum of each other, and not offer a double explanation (force + transference). My reason to favour that explanation is that it is simpler and works for the full range of cases, while the transference model only works for asymmetric interactions. Now, whether we accept this suggestion or not has no consequences for the point that simultaneous causation does not really lead to contradictions as long as we accept that exertion of influence and changes in state of motion are temporally extended phenomena.

Hansson Wahlberg develops another argument. Assuming that causal influence cannot be transmitted faster than light, he argues, then it takes time for the momentum to transfer across the spatial extension of the two combined bodies, wherefore causes cannot be simultaneous with their effects, at least if we are dealing with anything larger than point particles. So, even if we assume bodies to be rigid and that there is only action on contact, then because the momentum must be distributed across the whole spatial extension of each object, some of the momentum must have some distance to travel—however small—and this cannot happen instantaneously. My response is that he is again assuming that causation is transference, and that transfer cannot occur gradually. His argument poses no problem if momentum is not transferred but only changed as I have suggested. But it is not a problem even if we assume transference,

if the influence and the change are treated as activities that can occur gradually over time. If influence takes time rather than happens instantaneously, then there is plenty of time for the interaction to start slow and gradually increase as the action is propagated within each object, which is actually what happens in non-rigid objects, i.e. why they are compressed on contact. The conclusion is that on the interaction view I propose, and even on a transmission account that allows influence and change to occur gradually, it follows that:

(P7): Causes are simultaneous with their effects.

 
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