Causation as Simultaneous and Continuous

Here, I explain how all fundamental causation is simultaneous and continuous.* This is one of my better papers, but it’s somewhat neglected because “simultaneous causation” is treated as a fringe topic in metaphysics, which means that few people, even among those working on causation, would even look at the paper. If they did look at it, though, they’d find out that this is actually crucial to an understanding of the nature of causation in reality.

This is also my only co-authored paper. Ben Kovitz was a computer programmer friend of mine, who convinced me that simultaneous causation was real. I then proposed that we write up a paper on it. The main idea was his, but he wasn’t likely to actually write up a paper on his own.

[*From: “Causation as Simultaneous and Continuous,” Philosophical Quarterly 53 (2003): 556-65. Co-authored with Ben Kovitz.]

1. The Traditional (False) View of Causation

The traditional view is sequential: a cause happens, and then the effect happens, after the cause. Some people actually build this temporal order into their proposed definitions of causation. This is one way of getting the asymmetry of causation. (See Hume as well as Michael Tooley. Without the temporal priority, their accounts make causation non-asymmetric.)

Philosophers also traditionally represent laws of nature as having the form “Events of type A are always followed by events of type B”, or even “All A’s are B”.

… And Discrete Time

In Hume, that goes along with his discrete conception of time: he thinks that time consists of a discrete series of instants, where any given instant is immediately followed by a next instant. If that’s your view of time, then it makes sense that you’re going to think that the immediate effect of a given cause takes place at the next instant after the cause.

Extended Causal Processes

Traditionally, the idea of simultaneous causation, wherein the immediate effect happens at the same time as the cause, is controversial. One common argument: if the direct effect of a given cause always occurred at the same time as the cause, then there would be no extended causal sequences; the entire series of effects would happen instantaneously.

The Conservation Argument

A more subtle argument: Suppose billiard ball A hits billiard ball B. A imparts its momentum to B; i.e., A stops moving and B starts moving. If cause and effect were simultaneous, then there would have to be a moment at which A and B both had that momentum, which would violate conservation of momentum. To preserve conservation, it must be that B starts moving right after A stops. You can do a similar argument about energy transfers.

Physics

Some people say that modern physics shows that there’s no simultaneous causation. E.g., when you move your hand, this has a very slight gravitational effect on the moon. But that effect isn’t instantaneous; it takes some time (determined by the speed of light).

2. The Simultaneous (Correct) View of Causation

Time Is Continuous

Pace David Hume, the standard (correct) view of time is that it is a continuum. Among other things, that means that for any given instant in time, there is no next instant. For any two instants in time, there are always other instants in between them. E.g., between 12:00 and 1:00, there is 12:30. Between 12:00 and 12:30, there is 12:15. Between 12:00 and 12:15, there is 12:07:30. And so on, forever. Since there is no such thing as a “next instant”, it won’t do to say that a cause’s direct effect occurs at the next instant.

The Metaphysical Argument

Here is a metaphysical principle: X cannot directly influence anything at a time when X itself does not exist. For example, consider the serial killer Jack the Ripper, who lived in the 19th century. He died a long time ago and thus no longer exists (unless he had an immortal soul, but let’s leave that aside). Because he doesn’t even exist now, he can no longer hurt anyone, any more than Santa Claus can.

Qualification: He could be an indirect cause of some harm occurring today. E.g., he could have left behind some booby traps, which could possibly kill someone today. But he cannot directly kill anyone today, given that he no longer exists. I consider that self-evident.

Now suppose that you have a cause A and its direct effect, B. If they are not simultaneous, that means that B occurs at a time when A is no longer occurring. Which means A is producing its immediate effect at a time when A itself no longer exists. That’s impossible. So the effect has to be simultaneous with its immediate cause.

Causation in Physics

The claim about physics in sec. 1 is completely wrong. Modern physics, rather, refutes the sequential conception. Physics is all about simultaneous causation.

Take Newton’s second law, “F = ma”. Force and acceleration are functions of time, so the law is really:

              F(t) = m*a(t).

That says that the force acting at time t is proportional to the acceleration at time t. Not some later time. The law is not:

              F(t) = m*a(t+1)

which is what the sequential conception requires.

Btw, the essential point is preserved in relativity. In relativity, F=ma is revised to acknowledge that mass varies, so you get F = m*dv/dt + v*dm/dt. But again, the force at time t is going to be related, in that equation, to the mass, velocity, and rates of change of mass and velocity, at time t.

Another example, the Lorentz equation in electromagnetism:

              F = qE + qv x B

where F is the electromagnetic force on a particle, q is the particle’s charge, E is the electric field vector at the particle’s location, B is the magnetic field vector, and v is the velocity. (The “x” is the cross product symbol.) Again, the force at time t is related to the values of q, E, v, and B at time t, not at some earlier time. All the fundamental laws proposed in the last 300 years are like that. None of them say “Events of type A are always followed by events of type B”.

Broadly, the laws take the form of equations that relate the current configuration of a physical system to the rates of change of certain variables that feature in that same configuration. The current configuration acts as cause; those rates of change are the immediate effects.

Extended Sequences

What about the objection from sec. 1: How is it possible to get extended causal sequences?

First, note that the argument that all effects would occur at the same time depends on assuming that the effects from a given cause form a discrete series, so there’s an effect and then the next effect, and so on, in a countable sequence. In fact, there is a continuum of states between the initial cause and any later effect, since time is continuous. So just as there is no such thing as a “next” instant in time, there is no next effect in time.

There are direct effects, though, as I said above: the configuration at t directly causes a rate of change of that same configuration at t. Now, if you integrate that rate of change over an extended interval, you get a nonzero total change during the interval. This is mathematically implied by the law describing the rate of change. So these laws of simultaneous causation, involving rates of change, do not preclude extended causal processes; they entail the existence of extended causal processes.

The Conservation Argument

The conservation argument from sec. 1 above is also mistaken, in viewing the world in terms of discrete events, rather than continuous processes.

The collision between ball A and ball B is not an instantaneous event; it is a temporally extended (though very short) process. Let’s say the collision starts at time t1, and completes at time t2. During the interval from t1 to t2, A’s momentum is continuously decreasing, and at the same time, B’s momentum is continuously increasing. At any given instant in the interval, the sum of the two momenta is the same; at later times, it’s higher for B and lower for A. The two balls are each slightly deformed during the collision, and each is simultaneously exerting a force on the other.

I include a figure from the paper here.

Distinguishing Cause & Effect

A final issue: without relying on temporal priority, how can we distinguish cause & effect?

I don’t have an analysis of causation (there aren’t really any correct analyses in philosophy), so I’m not interested in finding a condition to put into an analysis to guarantee asymmetry.

As to how we know what is the cause and what the effect in the laws of nature: in some cases this is just intuitive. Intuitively, forces are things that cause accelerations, not vice versa. More generally, it’s the current configuration that causes the rate of change of that configuration. You can tell that, for one thing, because you can figure out the rates of change if given the current configuration, but not vice versa. E.g., if you know all the forces on X, you can determine X’s acceleration. But if you know the acceleration, you can’t thereby determine all the forces.