Thursday, September 9, 2010

Backwards causation

It is commonly thought that a cause C metaphysically cannot have an effect in its past. I see two simple ways of making sense of this principle in a relativistic framework:
  1. A cause can only have effects in the future half lightcone centered on it.
  2. A cause cannot have effects in the past half lightcone centered on it.
But I think neither of these is a plausible candidate for a metaphysical principle. Consider what (1) and (2) respectively say in a flat spacetime:
  1. A cause at (x,t) can only have an effect when the effect is at a spacetime location (y,u) such that |xy|<c(ut).
  2. A cause at (x,t) cannot have an effect at a spacetime location (y,u) when |xy|<c(tu).
But these just don't seem to be plausible candidates for a metaphysical principle, though I suppose one might think that they could be consequences of a physical principle. The same applies to the more complicated versions we'd need in a non-flat spacetime.
If we want (1) or (2) to be non-trivial metaphysical principles, we need to replace the references to lightcones by something of more metaphysical than physical significance. A plausible approach is to define the future half lightcone of a as the set of spacetime points states of affairs at which can be affected by a cause at a. But then (1) becomes simply the claim that causes can have effects only in spacetime, which is controversial and fails to capture the backwards causation intuition.
Now (2) is the claim that that a cause at a spacetime location b cannot affect anything at a spacetime location a when a is such that something at a could affect something at b. This is, in effect, a principle tailored to rule out causal loops. But if that's the intuition behind it, we might as well just say there are no causal loops, and be done with it. And if we do that, then we will have ruled out some, but not all, instances of backwards causation.

1 comment:

BernardZ said...


This is very much an example of circular logic as one of the planks of relativity is causality and Einstein never denied that FTL could exist.

Here are some interesting quotes from Einstein on the subject

"I did not say that a superluminal velocity is impossible; it is not impossible from the logical point of view, rather one can only say: if there existed a velocity that could really be conceived as the velocity
of propagation of a physical stimulus, then it would be possible to construct an arrangement that would allow
us to see at some place consequences of actions before we had innervated the thing by acts of volition. This seems to me to be something that has to be ruled out until proven otherwise, because it does not seem to be
in accord with our experience. Physical propagation velocities have nothing to do with the character of our
sense organs."

Towards the end of his life, probably under the influence of Goedel,
Einstein seems to have given up on causality.

"If the difference between past, present, and the future is an illusion, I.e., the four-dimensional spacetime is a 'block Universe' without
motion or change, then each individual is a collection of a myriad of selves, distributed along his history, each occurrence persisting on the
world line, experiencing indefinitely the particular event of that moment. Each of these momentary persons, according to our experience,
would possess memory of the previous ones, and would therefore believe himself identical with them; yet they would all exist separately, as
single pictures in a film. Placing the past, present, and future on the same footing this way, destroys the notion of the unity of the self,
rendering it a mere illusion as well."