Need some convincements on microcausality

[kof9595995]

Let me just quote peskin (Chap 2, causality) first:" ...So again we find that outside the lightcone, the propagation amplitude is exponentially vanishing but nonzero. To really discuss causality, however, we should not ask whether particles can propagate over spacelike intervals,but whether a measurement performed at one point can affect a measurement at another point whose separation from the first is spacelike. The simplest thing we could try to measure is the field phi(x), so we should compute the commutator [phi(x),phi(y)];if this commutator vanishes, one measurement cannot affect another..."
Two questions:
1. How can I justify that whether propagation amplitude is 0 has absolute nothing to do with causality?
2. When commutator is 0, how does it imply "one measurement cannot affect another" , I guess I need a more precise definition on "affect".

 

[azntoon]

1. The propagation amplitude is the probability that a particle can propagate over a given distance. As such, it does not directly address causality, which is concerned with how one event can affect another. In other words, even if a particle has a non-zero probability of propagating over a spacelike interval, this does not necessarily mean that the event at one point can “affect” the event at another point. 2. When the commutator [phi(x),phi(y)] is zero, it implies that the fields at two different points are independent of each other, i.e., one measurement (of the field at one point) cannot affect the result of a measurement at another point. This means that the two measurements are not correlated in any way, and thus they cannot affect each other.