Causality implies formal state collapse

TL;DR

This paper explores the implications of causality in physical theories, showing that state collapse across space-like separations implies superluminal signals or logical inconsistency, with stability results on theories with such signals.

Contribution

It establishes that causality enforces instantaneous state collapse across space-like separations and analyzes the structural stability of theories with superluminal or retrograde signals.

Findings

State collapse across space-like regions implies superluminal signals or inconsistency.

Theories with superluminal or retrograde signals are structurally stable and dense.

Time-like separations do not enforce the same collapse implications.

Abstract

A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: 1) the detector formally collapses physical states across space-like separations, 2) the detector enables superluminal signals, and 3) the theory becomes logically inconsistent. If such a theory admits autonomous evolving states, the space-like collapse must be instantaneous. Time-like separation does not allow such conclusions. We also prove some simple results on structural stability: within the set of all possible theories, under a weak empirical topology, the set of all theories with superluminal signals and the set of all theories with retrograde signals are both open and dense.