Retrocausality: A Toy Model
This toy system consists of three primitive nodes linked together as shown, each node comprising a meeting point of three edges. Each edge has one of three "flavors": A, B, or C. There are two basic rules that govern the dynamics of this toy system:[more]
1. Each node must be strictly inhomogeneous—that is, comprising three edges of different flavors—or strictly homogeneous—that is, three edges of the same flavor.
2. Successive homogeneous nodes are prohibited.
The flavor of each edge is displayed above and you can manipulate the input (yellow) flavors using the controls.
Interesting behavior emerges from the simple dynamics of the system. There exist some cases in which manipulation of solely the left input is correlated with changes in flavor of the internal (hidden) edges as well as the right output (and likewise for the left/right mirror image case).[less]
Beginning with the initial settings, manipulate the left and right inputs and observe the influence upon the respective left and right outputs. Observe that the hidden flavors do not change.
The center input can be used to randomize the flavors of the hidden edges (while remaining consistent with the dynamical laws of course!). Thus the selection of the same center input on different occasions may yield different hidden flavors.
Repeatedly reset the center input until the central node is homogeneous. The dynamical laws now prohibit either of the successive nodes from being homogeneous. If either the left or right inputs is now changed to the same flavor as the center input, the hidden state can no longer be homogeneous. Observe the subsequent influence throughout the system.
If it is assumed that the model represents a system evolving in time from bottom to top, then in the case where the central node is homogeneous, the internal flavors depend retrocausally on the left and right inputs. Note also that in such cases the output on the left depends on the input on the right (and vice versa) so the system displays a kind of nonlocality.
The interest of this toy model lies in whether the correlations that arise from this "retrocausal" behavior can be thought of as analogous to the correlations found in EPR-Bohm type experiments in quantum mechanics, supporting proposals for a retrocausal explanation in that case also.
For a full treatment of the model see http://arxiv.org/abs/0802.3230v1