Explaining Bell locally

In the Heisenberg picture of unitary quantum theory, Bell inequalities are violated with local elements of reality interacting locally. Here is how: Upon measuring her particle of the entangled pair, Alice—like other coupled systems—smoothly and locally evolves into two non-interacting versions of herself, each of which records a different outcome: she foliates . Everything that suitably interacts with the Alices foliates in turn, generating worlds which, for all practical purposes, remain distinct and autonomous. At spacelike separation, an analogous yet independent process occurs to Bob when he measures his particle, locally differentiating him and his surroundings into two non-interacting instances. To confirm the violation of Bell inequalities, Alice and Bob must further interact to produce a record of the joint outcomes. The record arises from the two local worlds of Alice, and those of Bob, and foliates into four instances: ‘ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>00</mml:mn> </mml:math> ’, ‘01’, ‘10’ and ‘11’. The outcomes that win the Clauser–Horne–Shimony–Holt (CHSH) game sum to a measure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>cos</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>⁡</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>8</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> .