**Bell's theorem** is a no-go theorem famous for drawing an important line in the sand between quantum mechanics (QM) and the world as we know it classically. In its simplest form, Bell's theorem states:

No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

When introduced in 1927, the philosophical implications of the new quantum theory were troubling to many prominent physicists of the day, including Albert Einstein. In a well known 1935 paper, he and co-authors Boris Podolsky and Nathan Rosen (collectively EPR) demonstrated by a paradox that QM was incomplete. This provided hope that a more complete (and less troubling) theory might one day be discovered. But that conclusion rested on the seemingly reasonable assumptions of locality and realism (together called "local realism" or "local hidden variables", often interchangeably). In the vernacular of Einstein: locality meant no instantaneous ("spooky") action at a distance; realism meant the moon is there even when not being observed. These assumptions were hotly debated within the physics community, notably with Nobel laureates Einstein on one side and Niels Bohr on the other.

In his groundbreaking 1964 paper, "On the Einstein Podolsky Rosen paradox", physicist John Stewart Bell presented an analogy (based on spin measurements on pairs of entangled electrons) to EPR's hypothetical paradox. Using their reasoning, he said, a choice of measurement setting here should not affect the outcome of a measurement there (and vice versa). After providing a mathematical formulation of locality and realism based on this, he showed specific cases where this would be inconsistent with the predictions of QM.

In experimental tests following Bell's example, now using quantum entanglement of photons instead of electrons, Alain Aspect et al. (1981) convincingly demonstrated that the predictions of QM are correct in this regard. While this does not demonstrate QM is complete, one is forced to reject either locality or realism (or both). That a relatively simple and elegant theorem could lead to this result has led Henry Stapp to call this theorem "the most profound in science".

Read more about Bell's Theorem: Overview, Importance of The Theorem, Bell Inequalities, Bell Inequalities Are Violated By Quantum Mechanical Predictions, Practical Experiments Testing Bell's Theorem, Theoretical Challenges, Cultural Impact, Final Remarks

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### Famous quotes containing the words theorem and/or bell:

“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

—Albert Camus (1913–1960)

“His are the quiet steeps of dreamland,

The waters of no-more-pain;

His ram’s *bell* rings ‘neath an arch of stars,

“Rest, rest, and rest again.””

—Walter De La Mare (1873–1956)