In this chapter I prove that the transition probabilities, which describe the dynamics of the actually possessed properties of systems, violate the assumption of Dynamical Autonomy for composite systems. And, related to this violation, it is also proved that the dynamics of the actually possessed properties is non-local in a quite explicit way.

Introduction

When I introduced the assumptions of Instantaneous and Dynamical Autonomy in Section 3.3, I motivated them by making an appeal to locality. In the case of Instantaneous Autonomy, I argued that a state of a system α should codify all the information about the property ascription to that system. For if a state does not codify all the information, it may happen that a change in the state of some distant system σ (I used the example of a far-away asteroid) means that the properties of α change as well. And this would make modal property ascriptions undesirably non-local. In the case of Dynamical Autonomy one can give a similar motivation. The state of a system α, as it evolves during a time interval i, should codify all the information about the simultaneous and sequential correlations between the properties ascribed to α in that interval i. For if the evolving state does not do so, it may happen that a change in a distant system changes the correlations between the properties of α as well.

Modal interpretations satisfy a number of the Autonomy assumptions. All modal interpretations satisfy Instantaneous Autonomy by construction. The transition probabilities derived in Section 8.2 prove that the bi and spectral modal interpretations satisfy Dynamical Autonomy for whole systems and that the atomic modal interpretation satisfies Dynamical Autonomy for atomic systems.