# Need some convincements on microcausality

• kof9595995
In summary: This is a more precise definition of “affect” in this context. In summary, the propagation amplitude being non-zero does not necessarily imply causality, and when the commutator of the field at two points is zero, it means that the measurements at these points are independent and cannot affect each other.
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".

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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.

## What is microcausality?

Microcausality is a principle in physics that states that the effects of a physical system cannot occur before their causes. In other words, the cause must precede the effect in time.

## Why is microcausality important?

Microcausality is important because it is a fundamental principle in our understanding of causality and how the universe operates. It helps us make predictions and explain the behavior of physical systems.

## How is microcausality tested?

Microcausality is typically tested through experiments and observations in the field of particle physics. These experiments involve looking at the interactions and reactions of particles to determine if the cause always precedes the effect.

## What happens if microcausality is violated?

If microcausality is violated, it would challenge our understanding of causality and have significant implications for our understanding of the universe. It could potentially lead to new theories and models to explain such violations.

## What are some examples of microcausality in action?

One example of microcausality in action is the decay of a radioactive atom, where the cause (the unstable nucleus) precedes the effect (the emission of particles). Another example is the propagation of electromagnetic waves, where the cause (the electric field) always precedes the effect (the magnetic field).

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