Gull's Theorem Revisited

Area of Science:

• Theoretical Physics
• Computer Science
• Information Theory

Background:

• Bell's theorem is a cornerstone of quantum mechanics, demonstrating the non-classical nature of reality.
• Previous interpretations of Bell's theorem have focused on quantum computing.
• Steve Gull proposed an alternative proof of Bell's theorem utilizing Fourier theory in 2016.

Purpose of the Study:

• To present and clarify Steve Gull's proof of Bell's theorem using Fourier theory.
• To reframe Bell's theorem as a no-go theorem for classical distributed computing.
• To address and fill gaps in Gull's original argument.

Main Methods:

• The study revisits Gull's Fourier-theoretic proof of Bell's theorem.
• It introduces a third computational element to complete the proof, representing a source of shared randomness.
• The method involves rewriting expectations conditional on hidden variables.

Main Results:

• The proof of Bell's theorem is completed by incorporating a third computer for shared randomness.
• Gull's argument is validated and extended, correcting identified misprints and gaps.
• The theorem is demonstrated to be a no-go theorem for classical distributed computing.

Conclusions:

• Bell's theorem, through Gull's Fourier-theoretic approach, has implications beyond quantum mechanics.
• The proof highlights the necessity of shared independent and identically distributed (i.i.d.) randomness in classical distributed computing.
• This work reframes the understanding of Bell's theorem within the context of classical computation and information theory.