Causality and the Interpretation of Quantum Mechanics
Kaixun Tu, Qing Wang
TL;DR
This work defines relativistic causality in quantum mechanics through region-local reduced density matrices, showing that local regions cannot be causally influenced in a way that violates light-speed constraints within quantum field theory. Building a detector-agnostic view, it argues that all physical operations are realized as local unitaries, bypassing detector-specific update rules and addressing Sorkin-type impossibilities. It then challenges the conventional Schrödinger’s cat paradox by highlighting intrinsic field entanglement, proposing a one-world interpretation where quantum mechanics is complete and produces definite macroscopic outcomes without wavefunction collapse, albeit with hidden variables that violate Statistical Independence. The framework aims to harmonize causality, nonlocality, and measurement in a relativistic setting and suggests that no-signaling constraints are preserved, while offering a deterministic yet relativity-compatible account of quantum measurements. It also identifies open problems in rigorously mapping quantum states to macroscopic states and in fully modeling detectors within quantum field theory, outlining a path for future quantitative development and empirical tests.
Abstract
From the ancient Einstein-Podolsky-Rosen paradox to the recent Sorkin-type impossible measurements problem, the contradictions between relativistic causality, quantum non-locality, and quantum measurement have persisted. Based on quantum field theory, our work provides a framework that harmoniously integrates these three aspects. This framework consists of causality expressed by reduced density matrices and an interpretation of quantum mechanics that considers quantum mechanics to be complete. Specifically, we use reduced density matrices to represent the local information of the quantum state and show that the reduced density matrices cannot evolve superluminally. Unlike recent approaches that address causality by introducing new operators to represent detectors, our perspective is that everything--including detectors, the environment, and even humans--is made up of the same fundamental fields. This viewpoint leads us to question the validity of the Schrodinger's cat paradox and motivates us to propose an interpretation of quantum mechanics that requires no extra assumptions and remains fully compatible with relativity.