Forward-backward stochastic simulations: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> -based model for measurement and Bell nonlocality consistent with weak local realistic premises

While Bell nonlocality can be explained through mechanisms such as retrocausality and superluminal influences, it is not clear why such mechanisms do not manifest at an everyday macroscopic level. In this paper, we show how measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling, and causal relations for macroscopic quantities. Considering the measurement of a field amplitude <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mover accent="true"> <a:mi>x</a:mi> <a:mo>̂</a:mo> </a:mover> </a:math> , we derive theorems that lead to an equivalence between a quantum phase-space probability distribution <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>Q</c:mi> <c:mo>(</c:mo> <c:mi>x</c:mi> <c:mo>,</c:mo> <c:mi>p</c:mi> <c:mo>,</c:mo> <c:mi>t</c:mi> <c:mo>)</c:mo> </c:mrow> </c:math> and stochastic trajectories for real amplitudes <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>x</d:mi> <d:mo>(</d:mo> <d:mi>t</d:mi> <d:mo>)</d:mo> </d:mrow> </d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>p</e:mi> <e:mo>(</e:mo> <e:mi>t</e:mi> <e:mo>)</e:mo> </e:mrow> </e:math> propagating backward and forward in time, respectively. We present forward-backward stochastic simulations that motivate a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>Q</f:mi> </f:math> -based objective-field model of reality. Amplification plays a key role in the measurement. With amplification, similar to decoherence, contributions due to interference become unobservable, leading to “branches” in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi>x</g:mi> </g:math> that correspond to distinct eigenvalues <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>λ</h:mi> </h:math> . This elucidates how the system evolves from a superposition to an eigenstate, from which Born's rule follows. For superposition states, we find that the backward and forward trajectories are connected, leading to “hidden loops.” We deduce a hybrid causal structure involving causal deterministic relations for amplified variables, along with microscopic noise inputs and hidden loops for unobservable quantities. Causal consistency is confirmed, removing grandfather-type paradoxes. The simulations allow evaluation of a state inferred for the system, conditioned on a particular branch <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>λ</i:mi> </i:math> , from which we deduce a model for projection and the collapse of the wave function. The theory is extended to Einstein-Podolsky-Rosen correlations and Bell nonlocality. We demonstrate consistency with three weak local realistic premises: (1) the existence of real properties (defined for the system after operations that fix measurement settings); (2) a partial locality implying no-signaling; (3) “elements of reality” that apply to the predictions of a system by a meter, once meter settings are fixed. A <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>Q</j:mi> </j:mrow> </j:math> -based hidden variable model and mechanism for Bell nonlocality is identified. Our work shows how forward-backward stochastic simulations lead to a hybrid causal structure, involving both deterministic causal relations and “hidden” stochastic loops, explaining measurement and entanglement, with paradoxes typically associated with retrocausality avoided.