Ax 4 in page 19 of Ticciati's QFT textbook.

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The discussion centers on the axiom relating to the interaction between two observations in the context of causality, specifically in Minkowski space. The statement asserts that if the squared distance between two points, |x-y|^2, is less than zero, then the commutation relation [φ(x), φ(y)] equals zero. However, the assertion that |x-y|^2 < 0 is always false raises confusion, as it implies that the condition cannot be satisfied, leading to questions about the implications of the axiom. The conversation highlights the significance of timelike intervals in the -+++ metric of Minkowski space, emphasizing the complexities of interpreting causality and commutation in quantum field theory.
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The axiom says:
"The interaction between two observations is constrained by causality
|x-y|^2 &lt;0 \Rightarrow [\phi(x),\phi(y)]=0
"

But |x-y|^2<0 is always false that means the if the condition applies then by simple logic the consequnet of the condition can occur or not occur, I don't understand this.
 
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The statement is about a timelike distance four-vector in Minkowski space. Its squared length is negative in the case of a -+++ metric.
 
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