Confounding Causality Principles: comment on R\'edei and san Pedro's "Distinguishing Causality Principles"

TL;DR

This paper defends the original causality principles SO1 and SO2 against critiques, clarifies misconceptions, corrects technical definitions, and discusses their relevance to algebraic quantum field theory.

Contribution

It provides a detailed rebuttal to critiques of SO1 and SO2, clarifies the principles' definitions, and assesses their applicability to AQFT.

Findings

The flaw in the original proof was a wording mistake, easily corrected.

The intuition that SO1 is stronger than SO2 is based on a false premise.

Cited results on causal conditions in AQFT are largely irrelevant or problematic.

Abstract

R\'edei and san Pedro discuss my "Comparing Causality Principles," their main aim being to distinguish reasonable weakened versions of two causality principles presented there, "SO1" and "SO2". They also argue that the proof that SO1 implies SO2 contains a flaw. Here, a reply is made to a number of points raised in their paper. It is argued that the "intuition" that SO1 should be stronger than SO2 is implicitly based on a false premise. It is pointed out that a similar weakening of SO2 was already considered in the original paper. The technical definition of the new conditions is shown to be defective. The argument against the stronger versions of SO1 and SO2 given by R\'edei and san Pedro is criticised. The flaw in the original proof is shown to be an easily corrected mistake in the wording. Finally, it is argued that some cited results on causal conditions in AQFT have little relevance to these issues, and are, in any case, highly problematic in themselves.