In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal “superquantum” correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.

The Greenberger-Horne-Zeilinger state is the most famous example of a state with multiparticle entanglement. In this article we describe a group theoretic framework we have been developing for understanding the entanglement in general states of two or more quantum particles. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)n). We consider both pure and mixed states and calculate the number of independent (...) parameters needed to describe such states up to this equivalence. We describe how the entanglement of states in a given equivalence class may be characterized by the stability group of the action of the group of local rotations on any of the states in the class. We also show how to calculate invariants under the group of local actions for both pure and mixed states. In the case of mixed states we are able to explicitly exhibit sets of invariants which allow one to determine whether two generic mixed states are equivalent up to local unitary transformations. (shrink)

Infants’ ability to monitor “sensorimotor contingencies,” i.e., the sensory effects of their own actions, is an important mechanism underlying learning. One method that has been used to investigate this is the “mobile paradigm,” in which a mobile above an infant’s crib is activated by motion of one of the infant’s limbs. Although successfully used in numerous experiments performed in infants’ homes to investigate memory and other types of learning, the paradigm seems less robust for demonstrating sensitivity to sensorimotor contingencies when (...) used in the laboratory. One purpose of the present work was to show that certain changes to the mobile paradigm would make it easier for infants to show their sensitivity to the contingency in the lab. In particular, we used proximal stimulation on infants’ wrists instead of the usual mobile, and our stimulation was coincident with the limbs that caused it. Our stimulation was either on or off, i.e., not modulated by the amount the infant moved. Finally, we used a “shaping” procedure to help the infant discover the contingency. In addition to these changes in the paradigm, by analyzing infants’ limb activity at 10-s resolution instead of the usual 1-min resolution, we were able to show that infants’ sensitivity to the contingency became apparent already within the first minute of establishment of the contingency. Finally, we showed how two alternate measures of sensitivity to contingency based on probability of repeated movements and on “stop and go” motion strategies may be of interest for future work. (shrink)