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

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The discussion centers on the axiom presented in page 19 of Ticciati's QFT textbook, which states that the interaction between two observations is constrained by causality, specifically expressed as |x-y|^2 < 0 leading to [\phi(x),\phi(y)] = 0. The assertion that |x-y|^2 < 0 is always false indicates that the condition cannot be satisfied, raising questions about the implications of this axiom. The statement pertains to a timelike distance four-vector in Minkowski space, where the squared length is negative under a -+++ metric, emphasizing the role of causality 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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