Colloquium: Bell’s theorem and locally mediated reformulations of quantum mechanics

Bell’s theorem rules out many potential reformulations of quantum mechanics, but within a generalized framework it does not exclude all locally mediated models. Such models describe the correlations between entangled particles as mediated by intermediate parameters that track the particle worldlines and respect Lorentz covariance. These locally mediated models require the relaxation of an arrow-of-time assumption that is typically taken for granted. Specifically, some of the mediating parameters in these models must functionally depend on measurement settings in their future, i.e., on input parameters associated with later times. This option, often called retrocausal, has been repeatedly pointed out in the literature, but the exploration of explicit locally mediated toy models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. These models provide a continuous and consistent description of events associated with spacetime locations, with aspects that are solved “all at once” rather than unfolding from the past to the future. The tension between quantum mechanics and relativity that is usually associated with Bell’s theorem does not occur here. Unlike in conventional quantum models, the number of parameters needed to specify the state of a system does not grow exponentially with the number of entangled particles. The promise of generalizing such models to account for all quantum phenomena is identified as a grand challenge.

Figure 1

The screening regions $\mathbf{S}$ used in different assumptions of locality. Given all modeled parameters in the screening region, a screened model will assign the same probabilities to parameters in region $\mathbf{1}$, regardless of additional knowledge of parameters in region $\mathbf{2}$. (a) shows the most general case of continuous action (CA); (b) breaks time symmetry by adding the no future-input dependence (NFID) assumption, and (c) references the light cones according to Bell’s screening assumption (BSA).

Figure 2

The essential geometry of a Bell-type experiment. The parameters $a$, $b$, and $c$ are inputs; the arrows indicate that their values come from outside the model. The parameters $A$ and $B$ are observable outputs. $\lambda$ is the set of all localized model parameters in the region $\mathbf{\Lambda }$, which screens regions $\mathbf{1}$ and $\mathbf{2}$ from the overlap of their backward light cones.