[Paper Review] Relativistic consistency rules out GRW-Pearle collapse schemes

Casey Blood|arXiv (Cornell University)|Apr 20, 2010

Quantum Mechanics and Applications11 references3 citations

TL;DR

This paper demonstrates that relativistic consistency—requiring measurement outcomes to be invariant across all inertial frames—rules out the GRW-Pearle spontaneous collapse models in quantum mechanics. By analyzing Lorentz transformations of collapse events, the author shows that these models predict frame-dependent detection outcomes, violating relativity and thus being physically inconsistent.

ABSTRACT

If the outcome recorded by a detector is required to be the same in all relativistically equivalent frames of reference, then a large class of collapse models, including the GRW-Pearle scheme, is ruled out.

Motivation & Objective

• To assess the compatibility of spontaneous collapse models, particularly GRW-Pearle, with the principles of special relativity.
• To investigate whether measurement outcomes in collapse models remain invariant under Lorentz transformations.
• To determine whether the requirement of relativistic invariance rules out specific collapse schemes.
• To analyze the transformation properties of collapse events across different inertial reference frames.

Proposed method

• The author constructs a gedankenexperiment involving a relativistic detector measuring a quantum system in a superposition.
• Lorentz transformations are applied to the spacetime coordinates of the collapse event to assess frame invariance.
• The analysis focuses on whether the detection outcome (e.g., which branch is selected) remains the same in all inertial frames.
• The GRW-Pearle model's stochastic collapse mechanism is examined under relativistic transformations, particularly the timing and location of collapse.
• The paper uses a relativistic framework to compare the predicted detection outcomes in different reference frames.
• The argument relies on the assumption that physical outcomes must be Lorentz-invariant, a cornerstone of special relativity.

Experimental results

Research questions

• RQ1 Do GRW-Pearle collapse models predict the same measurement outcome in all inertial reference frames?
• RQ2 Is the stochastic collapse process in GRW-Pearle compatible with Lorentz invariance?
• RQ3 Can a relativistic observer consistently describe the same physical outcome when the collapse event is frame-dependent?
• RQ4 What are the implications of frame-dependent collapse events for the physical consistency of spontaneous collapse theories?
• RQ5 Does the requirement of relativistic invariance rule out the GRW-Pearle class of models?

Key findings

• The GRW-Pearle collapse model predicts different detection outcomes in different inertial reference frames.
• Lorentz transformations of the collapse event lead to inconsistent measurement results across frames, violating relativistic consistency.
• The model's stochastic collapse mechanism is not invariant under Lorentz transformations, implying a fundamental conflict with special relativity.
• The paper concludes that any collapse model relying on a preferred frame or absolute time—like GRW-Pearle—is ruled out by relativistic consistency.
• The analysis shows that the collapse time and location are not Lorentz-invariant, leading to observable frame dependence in detection outcomes.
• Thus, the GRW-Pearle scheme cannot be a fundamental theory of quantum mechanics if it violates Lorentz invariance.