here, subscripts “a” and “b” distinguish the two particles, though it is more convenient and usual to refer to these particles as being in the possession of two experimentalists called alice and bob. the rules of quantum theory give predictions for the outcomes of measurements performed by the experimentalists. alice, for example, will measure her particle to be spin-up in an average of fifty percent of measurements. however, according to the copenhagen interpretation, alice's measurement causes the state of the two particles to collapse, so that if alice performs a measurement of spin in the z-direction, that is with respect to the basis formula_3, then bob's system will be left in one of the states formula_4. likewise, if alice performs a measurement of spin in the x-direction, that is, with respect to the basis formula_5, then bob's system will be left in one of the states formula_6. schrödinger referred to this phenomenon as "steering". this steering occurs in such a way that no signal can be sent by performing such a state update; quantum nonlocality cannot be used to send messages instantaneously and is therefore not in direct conflict with causality concerns in special relativity.