[Paper Review] Born's Rule, EPR, and the Free Will Theorem

Simon Kochen|arXiv (Cornell University)|Oct 2, 2017

Quantum Mechanics and Applications4 references3 citations

TL;DR

This paper argues that the EPR paradox does not imply non-locality when Born's Rule is properly applied, showing that quantum correlations can be consistent with Lorentz invariance and causality. By modeling particle responses as functions of spacelike-separated choices and using the Kochen-Specker theorem, it proves that particle responses cannot be predetermined, supporting the Free Will Theorem’s conclusion that particles have genuine freedom in their behavior.

ABSTRACT

Many physicists believe that the EPR experiment exhibits instantaneous non-local effects. I argue below that an application of Born's Rule to EPR shows no such instantaneous effects and that EPR is consistent with full Lorentz invariance. I then discuss how it is possible to understand the EPR correlations for non-commuting spin components without recourse to non-local effects. Finally, I use these results to discuss the Free Will Theorem, which I formulate in a new way.

Motivation & Objective

• To resolve the apparent conflict between EPR-type quantum correlations and Lorentz invariance by re-examining the role of Born's Rule.
• To demonstrate that EPR correlations do not imply superluminal signaling or backward causation when measurement outcomes are treated as probabilistic and context-dependent.
• To provide a causal framework for EPR where particle responses depend only on spacelike-past events, preserving causality.
• To use the Kochen-Specker theorem to prove that particle responses cannot be predetermined, supporting the Free Will Theorem.

Proposed method

• Applies Born's Rule to the EPR experiment, treating measurement outcomes as probabilistic projections onto spectral projectors.
• Models particle responses as functions of spacetime events earlier than the measurement in a given inertial frame, ensuring causality.
• Introduces functions $\theta_a^F$ and $\theta_b^G$ that depend only on choices and earlier events, excluding future influences.
• Uses the TWIN and SPIN axioms to enforce perfect anti-correlation and spin-1/2 constraints on orthogonal triples.
• Applies the Kochen-Specker theorem to show that no consistent assignment of definite values to all directions is possible, contradicting determinism.
• Imposes the LIN (Locality) axiom to enforce frame-independence of response functions, ensuring no superluminal dependence.

Experimental results

Research questions

• RQ1 Does the EPR experiment imply non-local or superluminal influences that violate Lorentz invariance?
• RQ2 Can EPR correlations be explained without assuming backward causation or non-locality?
• RQ3 Is it possible to define particle responses as functions of only spacelike-past events, preserving causality?
• RQ4 Can the Free Will Theorem be derived from EPR using the Kochen-Specker theorem and relativistic causality?
• RQ5 What constraints does the combination of Born's Rule, Lorentz invariance, and the EPR setup place on determinism in quantum mechanics?

Key findings

• The EPR experiment does not require non-local effects when Born's Rule is correctly applied, as measurement outcomes are probabilistic and context-dependent.
• Particle responses are functions of spacelike-past events only, ensuring no backward causation or superluminal signaling.
• The function $\theta_a^F(x,y,z)$ is independent of the distant measurement direction $w$, as required by the LIN axiom in a frame where $w$ is in the future.
• The function $\theta_b^G(w)$ is independent of the distant choices $x,y,z$, as required by the same LIN condition in a different frame.
• The requirement that $\theta_a^F(x,y,z) = (\theta_b^G(x), \theta_b^G(y), \theta_b^G(z))$ for all 40 orthogonal triples leads to a contradiction with the Kochen-Specker theorem.
• The contradiction implies that no consistent assignment of definite values to all spin components is possible, proving that particle responses are not predetermined — supporting the Free Will Theorem.